Publications of Paul S. Aspinwall    :chronological  alphabetical  by type listing:

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@article{fds322464,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {General mirror pairs for gauged linear sigma
             models},
   Journal = {The Journal of High Energy Physics},
   Volume = {2015},
   Number = {11},
   Year = {2015},
   Month = {November},
   url = {http://dx.doi.org/10.1007/JHEP11(2015)029},
   Doi = {10.1007/JHEP11(2015)029},
   Key = {fds322464}
}

@article{fds243265,
   Author = {Aspinwall, PS},
   Title = {Exoflops in two dimensions},
   Journal = {The Journal of High Energy Physics},
   Volume = {2015},
   Number = {7},
   Year = {2015},
   Month = {July},
   url = {http://dx.doi.org/10.1007/JHEP07(2015)104},
   Doi = {10.1007/JHEP07(2015)104},
   Key = {fds243265}
}

@article{fds243266,
   Author = {Aspinwall, PS and Gaines, B},
   Title = {Rational curves and (0, 2)-deformations},
   Journal = {Journal of Geometry and Physics},
   Volume = {88},
   Pages = {1-15},
   Year = {2015},
   Month = {February},
   ISSN = {0393-0440},
   url = {http://dx.doi.org/10.1016/j.geomphys.2014.09.012},
   Doi = {10.1016/j.geomphys.2014.09.012},
   Key = {fds243266}
}

@article{fds243264,
   Author = {Aspinwall, PS},
   Title = {Some applications of commutative algebra to string
             theory},
   Pages = {25-56},
   Booktitle = {Commutative Algebra: Expository Papers Dedicated to David
             Eisenbud on the Occasion of His 65th Birthday},
   Year = {2013},
   Month = {November},
   ISBN = {9781461452928},
   url = {http://dx.doi.org/10.1007/978-1-4614-5292-8_2},
   Abstract = {© 2013 Springer Science+Business Media New York. All rights
             reserved. String theory was first introduced as a model for
             strong nuclear interactions, then reinterpreted as a model
             for quantum gravity, and then all fundamental
             physics.},
   Doi = {10.1007/978-1-4614-5292-8_2},
   Key = {fds243264}
}

@article{fds303516,
   Author = {Addington, N and Aspinwall, PS},
   Title = {Categories of Massless D-Branes and del Pezzo
             Surfaces},
   Journal = {J. High Energy Phys. 7(176):39pp., 2013},
   Volume = {2013},
   Number = {176},
   Year = {2013},
   Month = {May},
   url = {http://arxiv.org/abs/1305.5767v2},
   Abstract = {In analogy with the physical concept of a massless D-brane,
             we define a notion of "Q-masslessness" for objects in the
             derived category. This is defined in terms of monodromy
             around singularities in the stringy Kahler moduli space and
             is relatively easy to study using spherical functors. We
             consider several examples in which del Pezzo surfaces and
             other rational surfaces in Calabi-Yau threefolds are
             contracted. For precisely the del Pezzo surfaces that can be
             written as hypersurfaces in weighted P3, the category of
             Q-massless objects is a "fractional Calabi-Yau" category of
             graded matrix factorizations.},
   Doi = {10.1007/JHEP07(2013)176},
   Key = {fds303516}
}

@article{fds212419,
   Author = {P.S. Aspinwall and M.R. Plesser},
   Title = {Elusive Worldsheet Instantons in Heterotic String
             Compactifications},
   Volume = {85},
   Pages = {33-52},
   Booktitle = {Proceedings of Symposia in Pure Mathematics},
   Year = {2012},
   url = {http://arxiv.org/abs/1106.2998},
   Key = {fds212419}
}

@article{fds243301,
   Author = {Aspinwall, PS and Melnikov, IV and Plesser, MR},
   Title = {(0,2) elephants},
   Journal = {Journal of High Energy Physics},
   Volume = {2012},
   Number = {1},
   Pages = {060},
   Year = {2012},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1007/JHEP01(2012)060},
   Abstract = {We enumerate massless E6 singlets for (0,2)-compactifications
             of the heterotic string on a Calabi-Yau threefold with the
             \standard embedding" in three distinct ways. In the large
             radius limit of the threefold, these singlets count
             deformations of the Calabi-Yau together with its tangent
             bundle. In the \small-radius" limit we apply Landau-Ginzburg
             methods. In the orbifold limit we use a combination of
             geometry and free field methods. In general these counts
             dier. We show how to identify states between these phases
             and how certain states vanish from the massless spectrum as
             one deforms the complex structure or Kahler form away from
             the Gepner point. The appearance of extra singlets for
             particular values of complex structure is explored in all
             three pictures, and our results suggest that this does not
             depend on the Kähler moduli. © SISSA 2012.},
   Doi = {10.1007/JHEP01(2012)060},
   Key = {fds243301}
}

@article{fds243302,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Quivers from Matrix Factorizations},
   Journal = {Communications in Mathematical Physics},
   Volume = {313},
   Number = {3},
   Pages = {607-633},
   Year = {2012},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-012-1520-1},
   Abstract = {We discuss how matrix factorizations offer a practical
             method of computing the quiver and associated superpotential
             for a hypersurface singularity. This method also yields
             explicit geometrical interpretations of D-branes (i. e.,
             quiver representations) on a resolution given in terms of
             Grassmannians. As an example we analyze some non-toric
             singularities which are resolved by a single ℙ 1 but have
             "length" greater than one. These examples have a much richer
             structure than conifolds. A picture is proposed that relates
             matrix factorizations in Landau-Ginzburg theories to the way
             that matrix factorizations are used in this paper to perform
             noncommutative resolutions. © 2012 Springer-Verlag.},
   Doi = {10.1007/s00220-012-1520-1},
   Key = {fds243302}
}

@article{fds303518,
   Author = {Aspinwall, PS},
   Title = {A McKay-Like Correspondence for (0,2)-Deformations},
   Volume = {18},
   Number = {4},
   Pages = {761-797},
   Year = {2011},
   Month = {October},
   url = {http://arxiv.org/abs/1110.2524v3},
   Abstract = {We present a local computation of deformations of the
             tangent bundle for a resolved orbifold singularity C^d/G.
             These correspond to (0,2)-deformations of (2,2)-theories. A
             McKay-like correspondence is found predicting the dimension
             of the space of first-order deformations from simple
             calculations involving the group. This is confirmed in two
             dimensions using the Kronheimer-Nakajima quiver
             construction. In higher dimensions such a computation is
             subject to nontrivial worldsheet instanton corrections and
             some examples are given where this happens. However, we
             conjecture that the special crepant resolution given by the
             G-Hilbert scheme is never subject to such corrections, and
             show this is true in an infinite number of cases. Amusingly,
             for three-dimensional examples where G is abelian, the
             moduli space is associated to a quiver given by the toric
             fan of the blow-up. It is shown that an orbifold of the form
             C^3/Z7 has a nontrivial superpotential and thus an
             obstructed moduli space.},
   Key = {fds303518}
}

@article{fds243303,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {Decompactifications and massless D-branes in hybrid
             models},
   Journal = {Journal of High Energy Physics},
   Volume = {2010},
   Number = {7},
   Pages = {078},
   Year = {2010},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1007/JHEP07(2010)078},
   Abstract = {A method of determining the mass spectrum of BPS D-branes in
             any phase limit of a gauged linear sigma model is
             introduced. A ring associated to monodromy is defined and
             one considers K-theory to be a module over this ring. A
             simple but interesting class of hybrid models with
             Landau-Ginzburg fibres over ℙ n are analyzed using special
             Kähler geometry and D-brane probes. In some cases the
             hybrid limit is an infinite distance in moduli space and
             corresponds to a decompactification. In other cases the
             hybrid limit is at a finite distance and acquires massless
             D-branes. An example studied appears to correspond to a
             novel theory of supergravity with an SU(2) gauge symmetry
             where the gauge and gravitational couplings are necessarily
             tied to each other. © SISSA 2010.},
   Doi = {10.1007/JHEP07(2010)078},
   Key = {fds243303}
}

@article{fds166462,
   Author = {P.S. Aspinwall},
   Title = {Probing Geometry with Stability Conditions},
   Year = {2009},
   Month = {May},
   url = {http://arxiv.org/abs/0905.3137},
   Key = {fds166462}
}

@book{fds166464,
   Author = {P.S. Aspinwall and Tom Bridgeland and Alastair Craw and Micheal
             Douglas, Mark Gross and Anton Kapustin and Greg Moore and Graeme
             Segal, Balazs Szendroi and Pelham Wilson},
   Title = {Dirichlet Branes and Mirror Symmetry},
   Publisher = {American Mathematical Society},
   Year = {2009},
   Key = {fds166464}
}

@article{fds243304,
   Author = {Aspinwall, PS},
   Title = {Topological D-branes and commutative algebra},
   Journal = {Communications in Number Theory and Physics},
   Volume = {3},
   Number = {3},
   Pages = {445-474},
   Year = {2009},
   ISSN = {1931-4523},
   url = {http://arxiv.org/abs/hep-th/0703279},
   Abstract = {We show that questions concerning the topological B-model on
             a Calabi-Yau manifold in the Landau-Ginzburg phase can be
             rephrased in the language of commutative algebra. This
             yields interesting and very practical methods for analyzing
             the model. We demonstrate how the relevant "Ext" groups and
             superpotentials can be computed efficiently by computer
             algebra packages such as Macaulay. This picture leads us to
             conjecture a general description of D-branes in linear sigma
             models in terms of triangulated categories. Each phase of
             the linear sigma model is associated with a different
             presentation of the category of D-branes.},
   Key = {fds243304}
}

@article{fds152804,
   Author = {P.S. Aspinwall},
   Title = {D-Branes on Toric Calabi-Yau Varieties},
   Year = {2008},
   url = {http://arxiv.org/abs/0806.2612},
   Key = {fds152804}
}

@article{fds152802,
   Author = {P.S. Aspinwall},
   Title = {The Landau-Ginzburg to Calabi-Yau Dictionary for
             D-Branes},
   Journal = {J.Math.Phys.},
   Volume = {48},
   Pages = {082304},
   Year = {2007},
   Key = {fds152802}
}

@article{fds243305,
   Author = {Aspinwall, PS},
   Title = {Landau-Ginzburg to Calabi-Yau dictionary for
             D-branes},
   Journal = {Journal of Mathematical Physics},
   Volume = {48},
   Number = {8},
   Pages = {082304},
   Year = {2007},
   ISSN = {0022-2488},
   url = {http://dx.doi.org/10.1063/1.2768185},
   Abstract = {Based on the work by Orlov (e-print arXiv:math.AG0503632),
             we give a precise recipe for mapping between B-type D-branes
             in a Landau-Ginzburg orbifold model (or Gepner model) and
             the corresponding large radius Calabi-Yau manifold. The
             D-branes in Landau-Ginzburg theories correspond to matrix
             factorizations and the D-branes on the Calabi-Yau manifolds
             are objects in the derived category. We give several
             examples including branes on quotient singularities
             associated with weighted projective spaces. We are able to
             confirm several conjectures and statements in the
             literature. © 2007 American Institute of
             Physics.},
   Doi = {10.1063/1.2768185},
   Key = {fds243305}
}

@article{fds243306,
   Author = {Aspinwall, PS and Maloney, A and Simons, A},
   Title = {Black hole entropy, marginal stability and mirror
             symmetry},
   Journal = {Journal of High Energy Physics},
   Volume = {2007},
   Number = {7},
   Pages = {034},
   Year = {2007},
   ISSN = {1126-6708},
   url = {http://dx.doi.org/10.1088/1126-6708/2007/07/034},
   Abstract = {We consider the superconformal quantum mechanics associated
             to BPS black holes in type IIB Calabi-Yau compactifications.
             This quantum mechanics describes the dynamics of D-branes in
             the near-horizon attractor geometry of the black hole. In
             many cases, the black hole entropy can be found by counting
             the number of chiral primaries in this quantum mechanics.
             Both the attractor mechanism and notions of marginal
             stability play important roles in generating the large
             number of microstates required to explain this entropy. We
             compute the microscopic entropy explicitly in a few
             different cases, where the theory reduces to quantum
             mechanics on the moduli space of special Lagrangians. Under
             certain assumptions, the problem may be solved by
             implementing mirror symmetry as three T-dualities: this is
             essentially the mirror of a calculation by Gaiotto,
             Strominger and Yin. In some simple cases, the calculation
             may be done in greater generality without resorting to
             conjectures about mirror symmetry. For example, the K3 × T2
             case may be studied precisely using the Fourier-Mukai
             transform. © SISSA 2007.},
   Doi = {10.1088/1126-6708/2007/07/034},
   Key = {fds243306}
}

@article{fds51429,
   Author = {P.S. Aspinwall},
   Title = {D-Branes, Pi-Stability and Theta-Stability},
   Volume = {401},
   Series = {Contemporary Mathematics},
   Booktitle = {Snowbird Lectures on String Geometry},
   Publisher = {AMS},
   Year = {2006},
   url = {http://arxiv.org/abs/hep-th/0407123},
   Key = {fds51429}
}

@article{fds243307,
   Author = {Aspinwall, PS and Fidkowski, LM},
   Title = {Superpotentials for quiver gauge theories},
   Journal = {The Journal of High Energy Physics},
   Volume = {2006},
   Number = {10},
   Pages = {047},
   Year = {2006},
   ISSN = {1029-8479},
   url = {http://dx.doi.org/10.1088/1126-6708/2006/10/047},
   Abstract = {We compute superpotentials for quiver gauge theories arising
             from marginal D-Brane decay on collapsed del Pezzo cycles S
             in a Calabi-Yau X. This is done using the machinery of A∞
             products in the derived category of coherent sheaves of X,
             which in turn is related to the derived category of S and
             quiver path algebras. We confirm that the superpotential is
             what one might have guessed from analyzing the moduli space,
             i.e., it is linear in the fields corresponding to the Ext2s
             of the quiver and that each such Ext 2 multiplies a
             polynomial in Ext1s equal to precisely the relation
             represented by the Ext2. © SISSA 2006.},
   Doi = {10.1088/1126-6708/2006/10/047},
   Key = {fds243307}
}

@article{fds243308,
   Author = {Aspinwall, PS and Katz, S},
   Title = {Computation of superpotentials for D-branes},
   Journal = {Communications in Mathematical Physics},
   Volume = {264},
   Number = {1},
   Pages = {227-253},
   Year = {2006},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/s00220-006-1527-6},
   Abstract = {We present a general method for the computation of
             tree-level superpotentials for the world-volume theory of
             B-type D-branes. This includes quiver gauge theories in the
             case that the D-brane is marginally stable. The technique
             involves analyzing the A ∞-structure inherent in the
             derived category of coherent sheaves. This effectively gives
             a practical method of computing correlation functions in
             holomorphic Chern-Simons theory. As an example, we give a
             more rigorous proof of previous results concerning 3-branes
             on certain singularities including conifolds. We also
             provide a new example.},
   Doi = {10.1007/s00220-006-1527-6},
   Key = {fds243308}
}

@article{fds303519,
   Author = {Aspinwall, PS and Kallosh, R},
   Title = {Fixing All Moduli for M-Theory on K3xK3},
   Journal = {JHEP},
   Volume = {0510},
   Pages = {001},
   Year = {2005},
   Month = {June},
   url = {http://arxiv.org/abs/hep-th/0506014v1},
   Abstract = {We analyze M-theory compactified on K3xK3 with fluxes
             preserving half the supersymmetry and its F-theory limit,
             which is dual to an orientifold of the type IIB string on
             $K3\times T^2/Z_2$. The geometry of attractive K3 surfaces
             plays a significant role in the analysis. We prove that the
             number of choices for the K3 surfaces is finite and we show
             how they can be completely classified. We list the
             possibilities in one case. We then study the instanton
             effects and see that they will generically fix all of the
             moduli. We also discuss situations where the instanton
             effects might not fix all the moduli.},
   Doi = {10.1088/1126-6708/2005/10/001},
   Key = {fds303519}
}

@article{fds43748,
   Author = {P.S. Aspinwall},
   Title = {An Analysis of Fluxes by Duality},
   Year = {2005},
   url = {http://arxiv.org/abs/hep-th/0504036},
   Key = {fds43748}
}

@article{fds43744,
   Author = {P.S. Aspinwall},
   Title = {D-Branes on Calabi-Yau Manifolds},
   Booktitle = {Progress in String Theory, TASI 2003 Lecture
             Notes},
   Publisher = {World Scientific},
   Year = {2005},
   url = {http://arxiv.org/abs/hep-th/0403166},
   Key = {fds43744}
}

@article{fds243300,
   Author = {Aspinwall, PS and Kallosh, R},
   Title = {Fixing all moduli for M-theory on K3×K3},
   Journal = {Journal of High Energy Physics},
   Number = {10},
   Pages = {1-20},
   Year = {2005},
   url = {http://dx.doi.org/10.1088/1126-6708/2005/10/001},
   Abstract = {We analyze M-theory compactified on K3 × K3 with fluxes
             preserving half the supersymmetry and its F-theory limit,
             which is dual to an orientifold of the type IIB string on K3
             × (T2/ℤ2). The geometry of attractive K3 surfaces plays a
             significant role in the analysis. We prove that the number
             of choices for the K3 surfaces is finite and we show how
             they can be completely classified. We list the possibilities
             in one case. We then study the instanton effects and see
             that they will generically fix all of the moduli. We also
             discuss situations where the instanton effects might not fix
             all the moduli. © SISSA 2005.},
   Doi = {10.1088/1126-6708/2005/10/001},
   Key = {fds243300}
}

@article{fds243309,
   Author = {Aspinwall, PS and Horja, RP and Karp, RL},
   Title = {Massless D-branes on Calabi-Yau threefolds and
             monodromy},
   Journal = {Communications in Mathematical Physics},
   Volume = {259},
   Number = {1},
   Pages = {45-69},
   Year = {2005},
   url = {http://dx.doi.org/10.1007/s00220-005-1378-6},
   Abstract = {We analyze the link between the occurrence of massless
             B-type D-branes for specific values of moduli and monodromy
             around such points in the moduli space. This allows us to
             propose a classification of all massless B-type D-branes at
             any point in the moduli space of Calabi-Yau's. This
             classification then justifies a previous conjecture due to
             Horja for the general form of monodromy. Our analysis is
             based on using monodromies around points in moduli space
             where a single D-brane becomes massless to generate
             monodromies around points where an infinite number become
             massless. We discuss the various possibilities within the
             classification. © Springer-Verlag 2005.},
   Doi = {10.1007/s00220-005-1378-6},
   Key = {fds243309}
}

@article{fds243298,
   Author = {Aspinwall, PS},
   Title = {The breakdown of topology at small scales},
   Journal = {Journal of High Energy Physics},
   Volume = {8},
   Number = {7},
   Pages = {453-463},
   Year = {2004},
   url = {http://arxiv.org/abs/hep-th/0312188v1},
   Abstract = {We discuss how a topology (the Zariski topology) on a space
             can appear to break down at small distances due to D-brane
             decay. The mechanism proposed coincides perfectly with the
             phase picture of Calabi-Yau moduli spaces. The topology
             breaks down as one approaches non-geometric phases. This
             picture is not without its limitations, which are also
             discussed. © SISSA/ISAS 2004.},
   Doi = {10.1088/1126-6708/2004/07/021},
   Key = {fds243298}
}

@article{fds243299,
   Author = {Aspinwall, PS and Melnikov, IV},
   Title = {D-branes on vanishing del Pezzo surfaces},
   Journal = {Journal of High Energy Physics},
   Volume = {8},
   Number = {12},
   Pages = {901-930},
   Year = {2004},
   url = {http://arxiv.org/abs/hep-th/0405134v2},
   Abstract = {We analyze in detail the case of a marginally stable D-Brane
             on a collapsed del Pezzo surface in a Calabi-Yau threefold
             using the derived category of quiver representations and the
             idea of aligned gradings. We show how the derived category
             approach to D-branes provides a straight-forward and
             rigorous construction of quiver gauge theories associated to
             such singularities. Our method shows that a procedure
             involving exceptional collections used elsewhere in the
             literature is only valid if some tachyon-inducing Ext3
             groups are zero. We then analyze in generality a large class
             of Seiberg dualities which arise from tilting equivalences.
             It follows that some (but not all) mutations of exceptional
             collections induce Seiberg duality in this context. The same
             tilting equivalence can also be used to remove unwanted Ext3
             groups and convert an unphysical quiver into a physical one.
             © SISSA/ISAS 2005.},
   Doi = {10.1088/1126-6708/2004/12/042},
   Key = {fds243299}
}

@article{fds243295,
   Author = {Aspinwall, PS},
   Title = {A point's point of view of stringy geometry},
   Journal = {Journal of High Energy Physics},
   Volume = {7},
   Number = {1},
   Pages = {17-31},
   Year = {2003},
   url = {http://arxiv.org/abs/hep-th/0203111v2},
   Abstract = {The notion of a "point" is essential to describe the
             topology of spacetime. Despite this, a point probably does
             not play a particularly distinguished rôle in any intrinsic
             formulation of string theory. We discuss one way to try to
             determine the notion of a point from a worldsheet point of
             view. The derived category description of D-branes is the
             key tool. The case of a flop is analyzed and II-stability in
             this context is tied in to some ideas of Bridgeland.
             Monodromy associated to the flop is also computed via
             II-stability and shown to be consistent with previous
             conjectures. © SISSA/ISAS 2003.},
   Doi = {10.1088/1126-6708/2003/01/002},
   Key = {fds243295}
}

@article{fds243297,
   Author = {Aspinwall, PS and Karp, RL},
   Title = {Solitons in Seiberg-Witten theory and D-branes in the
             derived category},
   Journal = {Journal of High Energy Physics},
   Volume = {7},
   Number = {4},
   Pages = {1119-1137},
   Year = {2003},
   url = {http://arxiv.org/abs/hep-th/0211121v1},
   Abstract = {We analyze the "geometric engineering" limit of a type II
             string on a suitable Calabi-Yau threefold to obtain an N = 2
             pure SU(2) gauge theory. The derived category picture
             together with II-stability of B-branes beautifully
             reproduces the known spectrum of BPS solitons in this case
             in a very explicit way. Much of the analysis is particularly
             easy since it can be reduced to questions about the derived
             category of ℙ1. © SISSA/ISAS 2003.},
   Doi = {10.1088/1126-6708/2003/04/049},
   Key = {fds243297}
}

@article{fds243296,
   Author = {Aspinwall, PS and Douglas, MR},
   Title = {D-brane stability and monodromy},
   Journal = {The Journal of High Energy Physics},
   Volume = {6},
   Number = {5},
   Pages = {739-773},
   Year = {2002},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/0110071},
   Abstract = {We review the idea of II-stability for B-type D-branes on a
             Calabi-Yau manifold. It is shown that the octahedral axiom
             from the theory of derived categories is an essential
             ingredient in the study of stability. Various examples in
             the context of the quintic Calabi-Yau threefold are studied
             and we plot the lines of marginal stability in several
             cases. We derive the conjecture of Kontsevich, Horja and
             Morrison for the derived category version of monodromy
             around a "conifold" point. Finally, we propose an
             application of these ideas to the study of supersymmetry
             breaking. © SISSA/ISAS 2002.},
   Key = {fds243296}
}

@article{fds243292,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {D-branes, discrete torsion and the McKay
             correspondence},
   Journal = {The Journal of High Energy Physics},
   Volume = {5},
   Number = {2},
   Pages = {XIX-25},
   Year = {2001},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/0009042},
   Abstract = {We analyze the D-branes of a type-IIB string theory on an
             orbifold singularity including the possibility of discrete
             torsion following the work of Douglas et al. First we prove
             some general results about the moduli space of a point
             associated to the "regular representation" of the orbifold
             group. This includes some analysis of the "wrapped branes"
             which necessarily appear when the orbifold singularity is
             not isolated. Next we analyze the stringy homology of the
             orbifold using the McKay correspondence and the relationship
             between K-theory and homology. We find that discrete torsion
             and torsion in this stringy homology are closely-related
             concepts but that they differ in general. Lastly we question
             to what extent the D-1 brane may be thought of as being dual
             to a string.},
   Key = {fds243292}
}

@article{fds243293,
   Author = {Aspinwall, PS},
   Title = {Some navigation rules for D-brane monodromy},
   Journal = {Journal of Mathematical Physics},
   Volume = {42},
   Number = {12},
   Pages = {5534-5552},
   Year = {2001},
   url = {http://dx.doi.org/10.1063/1.1409963},
   Abstract = {We explore some aspects of monodromies of D-branes in the
             Kähler moduli space of Calabi-Yau compactifications. Here a
             D-brane is viewed as an object of the derived category of
             coherent sheaves. We compute all the interesting monodromies
             in some nontrivial examples and link our work to recent
             results and conjectures concerning helices and mutations. We
             note some particular properties of the 0-brane. © 2001
             American Institute of Physics.},
   Doi = {10.1063/1.1409963},
   Key = {fds243293}
}

@article{fds243294,
   Author = {Aspinwall, PS and Lawrence, A},
   Title = {Derived categories and zero-brane stability},
   Journal = {The Journal of High Energy Physics},
   Volume = {5},
   Number = {8},
   Pages = {XIV-26},
   Year = {2001},
   ISSN = {1029-8479},
   Abstract = {We define a particular class of topological field theories
             associated to open strings and prove the resulting D-branes
             and open strings form the bounded derived category of
             coherent sheaves. This derivation is a variant of some ideas
             proposed recently by Douglas. We then argue that any 0-brane
             on any Calabi-Yau threefold must become unstable along some
             path in the Kähler moduli space. As a byproduct of this
             analysis we see how the derived category can be invariant
             under a birational transformation between
             Calabi-Yaus.},
   Key = {fds243294}
}

@article{fds243288,
   Author = {Aspinwall, PS and Katz, S and Morrison, DR},
   Title = {Lie groups, Calabi-Yau threefolds, and F-theory},
   Journal = {Advances in Theoretical and Mathematical
             Physics},
   Volume = {4},
   Number = {1},
   Pages = {1-24},
   Year = {2000},
   ISSN = {1095-0761},
   url = {http://arxiv.org/abs/hep-th/0002012},
   Abstract = {The F-theory vacuum constructed from an elliptic Calabi-Yau
             threefold with section yields an effective six-dimensional
             theory. The Lie algebra of the gauge sector of this theory
             and its representation on the space of massless
             hypermultiplets are shown to be determined by the
             intersection theory of the homology of the Calabi-Yau
             threefold. (Similar statements hold for M-theory and the
             type IIA string compactified on the threefold, where there
             is also a dependence on the expectation values of the
             Ramond-Ramond fields.) We describe general rules for
             computing the hypermultiplet spectrum of any F-theory
             vacuum, including vacua with non-simply-laced gauge groups.
             The case of monodromy acting on a curve of Aeven
             singularities is shown to be particularly interesting and
             leads to some unexpected rules for how 2-branes are allowed
             to wrap certain 2-cycles. We also review the peculiar
             numerical predictions for the geometry of elliptic
             Calabi-Yau threefolds with section which arise from anomaly
             cancellation in six dimensions.},
   Key = {fds243288}
}

@article{fds243290,
   Author = {Aspinwall, PS},
   Title = {A note on the equivalence of Vafa's and Douglas's picture of
             discrete torsion},
   Journal = {Journal of High Energy Physics},
   Volume = {4},
   Number = {12},
   Pages = {XXXVIII-6},
   Year = {2000},
   url = {http://arxiv.org/abs/hep-th/0009045},
   Abstract = {For a general non-abelian group action and an arbitrary
             genus worldsheet we show that Vafa's old definition of
             discrete torsion coincides with Douglas's D-brane definition
             of discrete torsion associated to projective
             representations.},
   Key = {fds243290}
}

@article{fds243291,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {Heterotic string corrections from the dual type-II
             string},
   Journal = {Journal of High Energy Physics},
   Volume = {4},
   Number = {4},
   Pages = {XXXIV-21},
   Year = {2000},
   url = {http://arxiv.org/abs/hep-th/9910248},
   Abstract = {We introduce a method of using the a dual type-IIA string to
             compute α′-corrections to the moduli space of heterotic
             string compactifications. In particular we study the
             hypermultiplet moduli space of a heterotic string on a K3
             surface. One application of this machinery shows that
             type-IIB strings compactified on a Calabi-Yau space suffer
             from worldsheet instantons, spacetime instantons and, in
             addition, "mixed" instantons which in a sense are both
             worldsheet and spacetime. As another application we look at
             the hyperkähler limit of the moduli space in which the K3
             surface becomes an ALE space. This is a variant of the
             "geometric engineering" method used for vector multiplet
             moduli space and should be applicable to a wide range of
             examples. In particular we reproduce Sen and Witten's result
             for the heterotic string on an A1 singularity and a trivial
             bundle and generalize this to a collection of E8 point-like
             instantons on an ALE space.},
   Key = {fds243291}
}

@article{fds303521,
   Author = {Aspinwall, PS},
   Title = {Compactification, Geometry and Duality: N=2},
   Year = {1999},
   Month = {December},
   url = {http://arxiv.org/abs/hep-th/0001001v2},
   Abstract = {These are notes based on lectures given at TASI99. We review
             the geometry of the moduli space of N=2 theories in four
             dimensions from the point of view of superstring
             compactification. The cases of a type IIA or type IIB string
             compactified on a Calabi-Yau threefold and the heterotic
             string compactified on K3xT2 are each considered in detail.
             We pay specific attention to the differences between N=2
             theories and N>2 theories. The moduli spaces of vector
             multiplets and the moduli spaces of hypermultiplets are
             reviewed. In the case of hypermultiplets this review is
             limited by the poor state of our current understanding. Some
             peculiarities such as ``mixed instantons'' and the
             non-existence of a universal hypermultiplet are
             discussed.},
   Key = {fds303521}
}

@article{fds243289,
   Author = {Aspinwall, PS and Plesser, MR},
   Title = {T-duality can fail},
   Journal = {The Journal of High Energy Physics},
   Volume = {3},
   Number = {8},
   Pages = {XI-18},
   Year = {1999},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9905036},
   Abstract = {We show that T-duality can be broken by non-perturbative
             effects in string coupling. The T-duality in question is
             that of the 2-torus when the heterotic string is
             compactified on K3xT2. This case is compared carefully to a
             situation where T-duality appears to work. A holonomy
             argument is presented to show that T-dualities (and general
             U-dualities) should only be expected for large amounts of
             supersymmetry. This breaking of R ↔ 1/R symmetry raises
             some interesting questions in string theory which we
             discuss. Finally we discuss how the classical modular group
             of a 2-torus appears to be broken too.},
   Key = {fds243289}
}

@article{fds243284,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Non-simply-connected gauge groups and rational points on
             elliptic curves},
   Journal = {The Journal of High Energy Physics},
   Volume = {1998},
   Number = {7},
   Pages = {XXII-15},
   Year = {1998},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9805206},
   Abstract = {We consider the F-theory description of non-simply-connected
             gauge groups appearing in the E8 × E8 heterotic string. The
             analysis is closely tied to the arithmetic of torsion points
             on an elliptic curve. The general form of the corresponding
             elliptic fibration is given for all finite subgroups of E8
             which are applicable in this context. We also study the
             closely-related question of point-like instantons on a K3
             surface whose holonomy is a finite group. As an example we
             consider the case of the heterotic string on a K3 surface
             having the E8 gauge symmetry broken to SU(9)/ℤ3 or (E6 ×
             SU(3))/ℤ3 by point-like instantons with ℤ3
             holonomy.},
   Key = {fds243284}
}

@article{fds243286,
   Author = {Aspinwall, PS and Donagi, RY},
   Title = {The heterotic string, The tangent bundle and derived
             categories},
   Journal = {Advances in Theoretical and Mathematical
             Physics},
   Volume = {2},
   Number = {5},
   Pages = {1041-1074},
   Year = {1998},
   ISSN = {1095-0761},
   url = {http://arxiv.org/abs/hep-th/9806094},
   Abstract = {We consider the compactification of the E8×E8 heterotic
             string on a K3 surface with "the spin connection embedded in
             the gauge group" and the dual picture in the type IIA string
             (or F-theory) on a Calabi-Yau threefold X. It turns out that
             the same X arises also as dual to a heterotic
             compactification on 24 point-like instantons. X is
             necessarily singular, and we see that this singularity
             allows the Ramond-Ramond moduli on X to split into distinct
             components, one containing the (dual of the heterotic)
             tangent bundle, while another component contains the
             point-like instantons. As a practical application we derive
             the result that a heterotic string compactified on the
             tangent bundle of a K3 with ADE singularities acquires
             nonperturbatively enhanced gauge symmetry in just the same
             fashion as a type IIA string on a singular K3 surface. On a
             more philosophical level we discuss how it appears to be
             natural to say that the heterotic string is compactified
             using an object in the derived category of coherent sheaves.
             This is necessary to properly extend the notion of T-duality
             to the heterotic string on a K3 surface. © 1998
             International Press.},
   Key = {fds243286}
}

@article{fds243287,
   Author = {Aspinwall, PS},
   Title = {Aspects of the hypermultiplet moduli space in string
             duality},
   Journal = {The Journal of High Energy Physics},
   Volume = {2},
   Number = {4},
   Pages = {XXIX-26},
   Year = {1998},
   ISSN = {1029-8479},
   url = {http://arxiv.org/abs/hep-th/9802194},
   Abstract = {A type IIA string (or F-theory) compactified on a Calabi-Yau
             threefold is believed to be dual to a heterotic string on a
             K3 surface times a 2-torus (or on a K3 surface). We consider
             how the resulting moduli space of hypermultiplets is
             identified between these two pictures in the case of the E8
             × E8 heterotic string. As examples we discuss SU(2)-bundles
             and G2-bundles on the K3 surface and the case of point-like
             instantons. We are lead to a rather beautiful identification
             between the integral cohomology of the Calabi-Yau threefold
             and some integral structures on the heterotic side somewhat
             reminiscent of mirror symmetry. We discuss the consequences
             for probing nonperturbative effects in the both the type IIA
             string and the heterotic string.},
   Key = {fds243287}
}

@article{fds243281,
   Author = {Aspinwall, PS},
   Title = {Point-like instantons and the Spin(32)/ℤ2
             heterotic string},
   Journal = {Nuclear Physics B},
   Volume = {496},
   Number = {1-2},
   Pages = {149-176},
   Year = {1997},
   url = {http://arxiv.org/abs/hep-th/9612108},
   Abstract = {We consider heterotic string theories compactified on a K3
             surface which lead to an unbroken perturbative gauge group
             of Spin(32)/ℤ2. All solutions obtained are combinations of
             two types of point-like instanton - one "simple type" as
             discovered by Witten and a new type associated to the
             "generalized second Stiefel-Whitney class" as introduced by
             Berkooz et al. The new type of instanton is associated to an
             enhancement of the gauge symmetry by Sp(4) and the addition
             of a massless tensor supermultiplet. It is shown that if
             four simple instantons coalesce at an orbifold point in the
             K3 surface then a massless tensor field appears which may be
             used to interpolate between the two types of instanton. By
             allowing various combinations of point-like instantons to
             coalesce, large gauge groups (e.g., rank 128) with many
             massless tensor supermultiplets result. The analysis is done
             in terms of F-theory. © 1997 Elsevier Science
             B.V.},
   Key = {fds243281}
}

@article{fds243285,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Point-like instantons on K3 orbifolds},
   Journal = {Nuclear Physics B},
   Volume = {503},
   Number = {3},
   Pages = {533-564},
   Year = {1997},
   Abstract = {The map between the moduli space of F-theory (or type II
             string) compactifications and heterotic string
             compactifications can be considerably simplified by using
             "stable degenerations". We discuss how this method applies
             to both the E8 × E8 and the Spin(32)/ℤ2 heterotic string.
             As a simple application of the method we derive some basic
             properties of the non-perturbative physics of collections of
             E8 or Spin(32)/ℤ2 point-like instantons sitting at ADE
             singularities on a K3 surface. © 1997 Elsevier Science
             B.V.},
   Key = {fds243285}
}

@article{fds303517,
   Author = {Aspinwall, PS and Gross, M},
   Title = {The SO(32) Heterotic String on a K3 Surface},
   Journal = {Phys.Lett. B},
   Volume = {387},
   Pages = {735-742},
   Year = {1996},
   Month = {May},
   url = {http://arxiv.org/abs/hep-th/9605131v2},
   Abstract = {The SO(32) heterotic string on a K3 surface is analyzed in
             terms of the dual theory of a type II string (or F-theory)
             on an elliptically fibred Calabi-Yau manifold. The results
             are in beautiful agreement with earlier work by Witten using
             very different methods. In particular, we find gauge groups
             of SO(32) x Sp(k) appearing at points in the moduli space
             identified with point-like instantons and see
             hypermultiplets in the (32,2k) representation becoming
             massless at the same time. We also discuss some aspects of
             the E8 x E8 case.},
   Doi = {10.1016/0370-2693(96)01095-7},
   Key = {fds303517}
}

@article{fds243276,
   Author = {Aspinwall, PS},
   Title = {An N = 2 dual pair and a phase transition},
   Journal = {Nuclear Physics B},
   Volume = {460},
   Number = {1},
   Pages = {57-76},
   Year = {1996},
   url = {http://dx.doi.org/10.1016/0550-3213(95)00611-7},
   Abstract = {We carefully analyze the N = 2 dual pair of string theories
             in four dimensions introduced by Ferrara, Harvey, Strominger
             and Vafa. The analysis shows that a second discrete degree
             of freedom must be switched on in addition to the known
             "Wilson line" to achieve a non-perturbatively consistent
             theory. We also identify the phase transition this model
             undergoes into another dual pair via a process analogous to
             a conifold transition. This provides the first known example
             of a phase transition which is understood from both the type
             II and the heterotic string picture.},
   Doi = {10.1016/0550-3213(95)00611-7},
   Key = {fds243276}
}

@article{fds243278,
   Author = {Aspinwall, PS and Louis, J},
   Title = {On the ubiquity of K3 fibrations in string
             duality},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {369},
   Number = {3-4},
   Pages = {233-242},
   Year = {1996},
   Abstract = {We consider the general case of N = 2 dual pairs of type
             IIA/heterotic string theories in four dimensions. We show
             that if the type IIA string in this pair can be viewed as
             having been compactified on a Calabi-Yau manifold in the
             usual way then this manifold must be of the form of a K3
             fibration. We also see how the bound on the rank of the
             gauge group of the perturbative heterotic string has a
             natural interpretation on the type IIA side.},
   Key = {fds243278}
}

@article{fds243279,
   Author = {Aspinwall, PS},
   Title = {Enhanced gauge symmetries and Calabi-Yau
             threefolds},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {371},
   Number = {3-4},
   Pages = {231-237},
   Year = {1996},
   Abstract = {We consider the general case of a type IIA string
             compactified on a Calabi-Yau manifold which has a heterotic
             dual description. It is shown that the nonabelian gauge
             symmetries which can appear nonperturbatively in the type II
             string but which are understood perturbatively in the
             heterotic string are purely a result of string-string
             duality in six dimensions. We illustrate this with some
             examples.},
   Key = {fds243279}
}

@article{fds243280,
   Author = {Aspinwall, PS},
   Title = {Some relationships between dualities in string
             theory},
   Journal = {Nuclear Physics B - Proceedings Supplements},
   Volume = {46},
   Number = {1-3},
   Pages = {30-38},
   Year = {1996},
   url = {http://dx.doi.org/10.1016/0920-5632(96)00004-7},
   Abstract = {Some relationships between string theories and
             eleven-dimensional supergravity are discussed and reviewed.
             We see how some relationships can be derived from others.
             The cases of N = 2 supersymmetry in nine dimensions and N =
             4 supersymmetry in four dimensions are discussed in some
             detail. The latter case leads to consideration of quotients
             of a K3 surface times a torus and to a possible peculiar
             relationship between eleven-dimensional supergravity and the
             heterotic strings in ten dimensions.},
   Doi = {10.1016/0920-5632(96)00004-7},
   Key = {fds243280}
}

@article{fds243282,
   Author = {Aspinwall, PS and Gross, M},
   Title = {Heterotic-heterotic string duality and multiple K3
             fibrations},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {382},
   Number = {1-2},
   Pages = {81-88},
   Year = {1996},
   Abstract = {A type IIA string compactified on a Calabi-Yau manifold
             which admits a K3 fibration is believed to be equivalent to
             a heterotic string in four dimensions. We study cases where
             a Calabi-Yau manifold can have more than one such fibration
             leading to equivalences between perturbatively inequivalent
             heterotic strings. This allows an analysis of an example in
             six dimensions due to Duff, Minasian and Witten and enables
             us to go some way to prove a conjecture by Kachru and Vafa.
             The interplay between gauge groups which arise
             perturbatively and nonperturbatively is seen clearly in this
             example. As an extreme case we discuss a Calabi-Yau manifold
             which admits an infinite number of K3 fibrations leading to
             infinite set of equivalent heterotic strings.},
   Key = {fds243282}
}

@article{fds243283,
   Author = {Aspinwall, PS and Morrison, DR and Gross, M},
   Title = {Stable singularities in string theory},
   Journal = {Communications in Mathematical Physics},
   Volume = {178},
   Number = {1},
   Pages = {115-134},
   Year = {1996},
   Abstract = {We study a topological obstruction of a very stringy nature
             concerned with deforming the target space of an N = 2
             non-linear σ-model. This target space has a singularity
             which may be smoothed away according to the conventional
             rules of geometry, but when one studies the associated
             conformal field theory one sees that such a deformation is
             not possible without a discontinuous change in some of the
             correlation functions. This obstruction appears to come from
             torsion in the homology of the target space (which is seen
             by deforming the theory by an irrelevant operator). We
             discuss the link between this phenomenon and orbifolds with
             discrete torsion as studied by Vafa and Witten.},
   Key = {fds243283}
}

@article{fds243274,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {U-duality and integral structures},
   Journal = {Physics Letters B},
   Volume = {355},
   Number = {1-2},
   Pages = {141-149},
   Year = {1995},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(95)00745-7},
   Abstract = {We analyze the U-duality group of the case of a type II
             superstring compactified to four dimensions on a K3 surface
             times a torus. The various limits of this theory are
             considered which have interpretations as type IIA and IIB
             superstrings, the heterotic string, and eleven-dimensional
             supergravity, allowing all these theories to be directly
             related to each other. The integral structure which appears
             in the Ramond-Ramond sector of the type II superstring is
             related to the quantum cohomology of general Calabi-Yau
             threefolds which allows the moduli space of type II
             superstring compactifications on Calabi-Yau manifolds to be
             analyzed. © 1995.},
   Doi = {10.1016/0370-2693(95)00745-7},
   Key = {fds243274}
}

@article{fds243275,
   Author = {Aspinwall, PS and Greene, BR},
   Title = {On the geometric interpretation of N = 2 superconformal
             theories},
   Journal = {Nuclear Physics B},
   Volume = {437},
   Number = {1},
   Pages = {205-227},
   Year = {1995},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(94)00571-U},
   Abstract = {We clarify certain important issues relevant for the
             geometric interpretation of a large class of N= 2
             superconformal theories. By fully exploiting the phase
             structure of these theories (discovered in earlier works) we
             are able to clearly identify their geometric content. One
             application is to present a simple and natural resolution to
             the question of what constitutes the mirror of a rigid
             Calabi-Yau manifold. We also discuss some other models with
             unusual phase diagrams that highlight some subtle features
             regarding the geometric content of conformal theories. ©
             1995 Elsevier Science B.V. All rights reserved.},
   Doi = {10.1016/0550-3213(94)00571-U},
   Key = {fds243275}
}

@article{fds243277,
   Author = {Aspinwall, PS},
   Title = {Enhanced gauge symmetries and K3 surfaces},
   Journal = {Physics Letters B},
   Volume = {357},
   Number = {3},
   Pages = {329-334},
   Year = {1995},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(95)00957-M},
   Abstract = {String-string duality dictates that type IIA strings
             compactified on a K3 surface acquire non-abelian gauge
             groups for certain values of the K3 moduli. We argue that,
             contrary to expectation, the theories for which such
             enhanced gauge symmetries appear are not orbifolds in the
             string sense. For a specific example we show that a theory
             with enhanced gauge symmetry and an orbifold theory have the
             same classical K3 surface as a target space but the value of
             the "B-field" differs. This raises the possibility that the
             conformal field theory associated to a string theory with an
             enhanced gauge group is badly behaved in some way. ©
             1995.},
   Doi = {10.1016/0370-2693(95)00957-M},
   Key = {fds243277}
}

@article{fds243269,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Measuring small distances in N = 2 sigma
             models},
   Journal = {Nuclear Physics B},
   Volume = {420},
   Number = {1-2},
   Pages = {184-242},
   Year = {1994},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(94)90379-4},
   Abstract = {We analyze global aspects of the moduli space of Kähler
             forms for N = (2,2) conformal σ-models. Using algebraic
             methods and mirror symmetry we study extensions of the
             mathematical notion of length (as specified by a Kähler
             structure) to conformal field theory and calculate the way
             in which lengths change as the moduli fields are varied
             along distinguished paths in the moduli space. We find
             strong evidence supporting the notion that, in the robust
             setting of quantum Calabi-Yau moduli space, string theory
             restricts the set of possible Kähler forms by enforcing
             "minimal length" scales, provided that topology change is
             properly taken into account. Some lengths, however, may
             shrink to zero. We also compare stringy geometry to
             classical general relativity in this context. ©
             1994.},
   Doi = {10.1016/0550-3213(94)90379-4},
   Key = {fds243269}
}

@article{fds243270,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Chiral rings do not suffice: N=(2,2) theories with nonzero
             fundamental group},
   Journal = {Physics Letters B},
   Volume = {334},
   Number = {1-2},
   Pages = {79-86},
   Year = {1994},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(94)90594-0},
   Abstract = {The Kähler moduli space of a particular
             non-simply-connected Calabi-Yau manifold is mapped out using
             mirror symmetry. It is found that, for the model considered,
             the chiral ring may be identical for different associated
             conformal field theories. This ambiguity is explained in
             terms of both A-model and B-model language. It also provides
             an apparent counterexample to the global Torelli problem for
             Calabi-Yau threefolds. © 1994.},
   Doi = {10.1016/0370-2693(94)90594-0},
   Key = {fds243270}
}

@article{fds243271,
   Author = {Aspinwall, PS},
   Title = {Minimum distances in non-trivial string target
             spaces},
   Journal = {Nuclear Physics B},
   Volume = {431},
   Number = {1-2},
   Pages = {78-96},
   Year = {1994},
   Abstract = {The idea of minimum distance, familiar from R ↔ 1/R
             duality when the string target space is a circle, is
             analyzed for less trivial geometries. The particular
             geometry studied is that of a blown-up quotient singularity
             within a Calabi-Yau space and mirror symmetry is used to
             perform the analysis. It is found that zero distances can
             appear but that in many cases this requires other distances
             within the same target space to be infinite. In other cases
             zero distances can occur without compensating infinite
             distances.},
   Key = {fds243271}
}

@article{fds243272,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Space-time topology change and stringy geometry
             a},
   Journal = {Journal of Mathematical Physics},
   Volume = {35},
   Number = {10},
   Pages = {5321-5337},
   Year = {1994},
   ISSN = {0022-2488},
   Abstract = {Recent work which has significantly honed the geometric
             understanding and interpretation of the moduli space of
             certain N=2 superconformal field theories is reviewed. This
             has resolved some important issues in mirror symmetry and
             has also established that string theory admits physically
             smooth processes which can result in a change in topology of
             the spatial universe. Recent work which illuminates some
             properties of physically related theories associated with
             singular spaces such as orbifolds is described. © 1994
             American Institute of Physics.},
   Key = {fds243272}
}

@article{fds243273,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Calabi-Yau moduli space, mirror manifolds and spacetime
             topology change in string theory},
   Journal = {Nuclear Physics B},
   Volume = {416},
   Number = {2},
   Pages = {414-480},
   Year = {1994},
   Abstract = {We analyze the moduli spaces of Calabi-Yau three-folds and
             their associated conformally invariant nonlinear σ-models
             and show that they are described by an unexpectedly rich
             geometrical structure. Specifically, the Kahler sector of
             the moduli space of such Calabi-Yau conformal theories
             admits a decomposition into adjacent domains some of which
             correspond to the (complexified) Kahler cones of
             topologically distinct manifolds. These domains are
             separated by walls corresponding to singular Calabi-Yau
             spaces in which the spacetime metric has degenerated in
             certain regions. We show that the union of these domains is
             isomorphic to the complex structure moduli space of a single
             topological Calabi-Yau space - the mirror. In this way we
             resolve a puzzle for mirror symmetry raised by the apparent
             asymmetry between the Kahler and complex structure moduli
             spaces of a Calabi-Yau manifold. Furthermore, using mirror
             symmetry, we show that we can interpolate in a physically
             smooth manner between any two theories represented by
             distinct points in the Kahler moduli space, even if such
             points correspond to topologically distinct spaces.
             Spacetime topology change in string theory, therefore, is
             realized by the most basic operation of deformation by a
             truly marginal operator. Finally, this work also yields some
             important insights on the nature of orbifolds in string
             theory.},
   Key = {fds243273}
}

@booklet{Aspinwall93,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {The Monomial-Divisor Mirror Map},
   Journal = {Internat. Math. Res. Notices (1993), 319-337},
   Volume = {72},
   Number = {3},
   Pages = {319 -- 337},
   Year = {1993},
   Month = {September},
   url = {http://arxiv.org/abs/alg-geom/9309007v1},
   Abstract = {For each family of Calabi-Yau hypersurfaces in toric
             varieties, Batyrev has proposed a possible mirror partner
             (which is also a family of Calabi-Yau hypersurfaces). We
             explain a natural construction of the isomorphism between
             certain Hodge groups of these hypersurfaces, as predicted by
             mirror symmetry, which we call the monomial-divisor mirror
             map. We indicate how this map can be interpreted as the
             differential of the expected mirror isomorphism between the
             moduli spaces of the two Calabi-Yau manifolds. We formulate
             a very precise conjecture about the form of that mirror
             isomorphism, which when combined with some earlier
             conjectures of the third author would completely specify it.
             We then conclude that the moduli spaces of the nonlinear
             sigma models whose targets are the different birational
             models of a Calabi-Yau space should be connected by analytic
             continuation, and that further analytic continuation should
             lead to moduli spaces of other kinds of conformal field
             theories. (This last conclusion was first drawn by
             Witten.)},
   Key = {Aspinwall93}
}

@article{fds322465,
   Author = {Aspinwall, PS and Morrison, DR and Greene, BR},
   Title = {The monomial-divisor mirror map},
   Journal = {International Mathematics Research Notices},
   Volume = {1993},
   Number = {12},
   Pages = {319-337},
   Year = {1993},
   Month = {January},
   url = {http://dx.doi.org/10.1155/S1073792893000376},
   Doi = {10.1155/S1073792893000376},
   Key = {fds322465}
}

@booklet{Aspinwall93a,
   Author = {Aspinwall, PS and Morrison, DR},
   Title = {Topological field theory and rational curves},
   Journal = {Communications in Mathematical Physics},
   Volume = {151},
   Number = {2},
   Pages = {245-262},
   Year = {1993},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF02096768},
   Abstract = {We analyze the quantum field theory corresponding to a
             string propagating on a Calabi-Yau threefold. This theory
             naturally leads to the consideration of Witten's topological
             non-linear σ-model and the structure of rational curves on
             the Calabi-Yau manifold. We study in detail the case of the
             world-sheet of the string being mapped to a multiple cover
             of an isolated rational curve and we show that a natural
             compactification of the moduli space of such a multiple
             cover leads to a formula in agreement with a conjecture by
             Candelas, de la Ossa, Green and Parkes. © 1993
             Springer-Verlag.},
   Doi = {10.1007/BF02096768},
   Key = {Aspinwall93a}
}

@booklet{Aspinwall93,
   Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
   Title = {Multiple mirror manifolds and topology change in string
             theory},
   Journal = {Physics Letters B},
   Volume = {303},
   Number = {3-4},
   Pages = {249-259},
   Year = {1993},
   ISSN = {0370-2693},
   url = {http://dx.doi.org/10.1016/0370-2693(93)91428-P},
   Abstract = {We use mirror symmetry to establish the first concrete arena
             of spacetime topology change in string theory. In
             particular, we establish that the quantum theories based on
             certain nonlinear sigma models with topologically distinct
             target spaces can be smoothly connected even though
             classically a physical singularity would be encountered. We
             accomplish this by rephrasing the description of these
             nonlinear sigma models in terms of their mirror manifold
             partners - a description in which the full quantum theory
             can be described exactly using lowest order geometrical
             methods. We establish that, for the known class of mirror
             manifolds, the moduli space of the corresponding conformal
             field theory requires not just two but numerous
             topologically distinct Calabi-Yau manifolds for its
             geometric interpretation. A single family of continously
             connected conformal theories thereby probes a host of
             topologically distinct geometrical spaces giving rise to
             multiple mirror manifolds. © 1993.},
   Doi = {10.1016/0370-2693(93)91428-P},
   Key = {Aspinwall93}
}

@booklet{Aspinwall91a,
   Author = {Aspinwall, PS and Lütken, CA},
   Title = {Geometry of mirror manifolds},
   Journal = {Nuclear Physics B},
   Volume = {353},
   Number = {2},
   Pages = {427-461},
   Year = {1991},
   Abstract = {We analyze the mirror manifold hypothesis in one and three
             dimensions using the simplest available representations of
             the N = 2 superconformai algebra. The symmetries of these
             tensor models can be divided out to give an explicit
             representation of the mirror, and we give a simple group
             theoretical algorithm for determining which symmetries
             should be used. We show that the mirror of a superconformai
             field theory does not always have a geometrical
             interpretation, but when it does, deformations of complex
             structure of one manifold are reflected in deformations of
             the Kähler form of the mirror manifold, and we show how the
             large radius limit of a manifold corresponds to a large
             complex structure limit in the mirror manifold. The mirror
             of the Tian-Yau three generation model is constructed both
             as a conformal field theory and as an algebraic variety with
             Euler number six. The Hodge numbers of this manifold are
             fixed, but the intersection numbers are highly ambiguous,
             presumably reflecting a rich structure of multicritical
             points in the moduli space of the field theory.},
   Key = {Aspinwall91a}
}

@booklet{Aspinwall91,
   Author = {Aspinwall, PS and Lütken, CA},
   Title = {Quantum algebraic geometry of superstring
             compactifications},
   Journal = {Nuclear Physics B},
   Volume = {355},
   Number = {2},
   Pages = {482-510},
   Year = {1991},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(91)90123-F},
   Abstract = {We investigate the algebrao-geometric structure which is
             inherent in 2-dimensional conformally invariant quantum
             field theories with N=2 supersymmetry, and its relation to
             the Calabi-Yau manifolds which appear in the so-called
             "large radius limit". Based on a careful comparison of the
             Kähler cone of Calabi-Yau manifolds and the moduli space of
             marginal chiral fields in string theory, we give a precise
             definition of this limit. The possibility of "flopping"
             between manifolds of different topology implies that the
             large radius limit of a given conformal model is ambiguous,
             and that the instantons in string theory could smooth out
             some of the singularities present in the classical moduli
             space. Since the mirror symmetry implies that the duality
             group of the stringy moduli space in a topological basis is
             at least Sp(b-3, Z)×Sp(b13, Z), we are able to identify the
             generalization of the "R → 1/R" symmetry in c=1 models to
             any (2,2) model. © 1991.},
   Doi = {10.1016/0550-3213(91)90123-F},
   Key = {Aspinwall91}
}

@article{fds243268,
   Author = {Aspinwall, P},
   Title = {(2, 2)-Superconformal field theories near orbifold
             points},
   Journal = {Communications in Mathematical Physics},
   Volume = {128},
   Number = {3},
   Pages = {593-611},
   Year = {1990},
   ISSN = {0010-3616},
   url = {http://dx.doi.org/10.1007/BF02096875},
   Abstract = {A thorough analysis of the "blowing-up" modes of the ℤ6
             based on the Lie algebra A2⊕D4 is presented. We discover
             that the descriptions of these modes in the language of
             superconformal field theory and Calabi-Yau compactification
             are not immediately in agreement. A solution to this
             apparent inconsistency is offered which leads to the
             possibility of differentiably distinct Calabi-Yau manifolds
             giving isomorphic physics. © 1990 Springer-Verlag.},
   Doi = {10.1007/BF02096875},
   Key = {fds243268}
}

@booklet{Aspinwall90,
   Author = {Aspinwall, PS and Lütken, CA and Ross, GG},
   Title = {Construction and couplings of mirror manifolds},
   Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
             High-Energy Physics},
   Volume = {241},
   Number = {3},
   Pages = {373-380},
   Year = {1990},
   Abstract = {We present an analysis of the conjectured existence of
             Calabi-Yau "mirror manifolds" for the case where the
             starting manifold is Y4,5. We construct mirror pairs with
             equal but opposite values for the Euler characteristic and
             the Hodge numbers h2,1 and h1,1 interchanged. In one
             particular example we show that the couplings of (1,1)-forms
             equal the couplings of (2,1)-forms in the mirror manifold,
             provided that a suitable limit is taken of the complex
             structure which corresponds to the large-radius limit
             appropriate for the mirror manifold. This leads to a
             determination, via deformation theory, of corrections to the
             topologically determined couplings of the
             (1,1)-forms.},
   Key = {Aspinwall90}
}

@booklet{Aspinwall87,
   Author = {ASPINWALL, PS and GREENE, BR and KIRKLIN, KH and MIRON,
             PJ},
   Title = {SEARCHING FOR 3-GENERATION CALABI-YAU MANIFOLDS},
   Journal = {Nuclear Physics B},
   Volume = {294},
   Number = {1},
   Pages = {193-222},
   Year = {1987},
   Month = {November},
   ISSN = {0550-3213},
   url = {http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1987K348000010&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=47d3190e77e5a3a53558812f597b0b92},
   Doi = {10.1016/0550-3213(87)90579-7},
   Key = {Aspinwall87}
}

@article{fds243267,
   Author = {Aspinwall, PS and Greene, BR and Kirklin, KH and Miron,
             PJ},
   Title = {Searching for three-generation Calabi-Yau
             manifolds},
   Journal = {Nuclear Physics B},
   Volume = {294},
   Number = {C},
   Pages = {193-222},
   Year = {1987},
   ISSN = {0550-3213},
   url = {http://dx.doi.org/10.1016/0550-3213(87)90579-7},
   Abstract = {All possible Calabi-Yau manifolds realisable as complete
             intersections and quotients of complete intersections by
             projectively-inherited symmetries are considered. We develop
             a stringent set of criteria with which to exhaustively
             search this huge class for three-generation manifolds. We
             find only one manifold meeting our conditions - namely the
             first manifold discovered by Yau. In addition it is shown
             that all known three-generation Calabi-Yau manifolds are
             either diffeomorphic to this one example or ill-defined. ©
             1987.},
   Doi = {10.1016/0550-3213(87)90579-7},
   Key = {fds243267}
}

@article{fds10130,
   Author = {Paul S. Aspinwall and Albion Lawrence},
   Title = {Derived Categories and 0-Brane Stability},
   Journal = {J. High Energy Phys. 08 (2001) 004},
   url = {http://arxiv.org/abs/hep-th/0104147},
   Key = {fds10130}
}

@article{fds8976,
   Author = {Paul S Aspinwall},
   Title = {String Theory and Duality},
   Journal = {Doc. Math. J. DMV Extra Volume ICM II (1998)
             229-238.},
   url = {http://arxiv.org/abs/math/9809004},
   Key = {fds8976}
}

@article{fds8970,
   Author = {Paul S Aspinwall},
   Title = {K3 Surfaces and String Duality},
   Journal = {in C. Esthimiou and B. Greene, editors, "Fields, Strings and
             Duality, TASI 1996", pages 421-540, World Scientific,
             1997.},
   url = {http://arxiv.org/abs/hep-th/9611137},
   Key = {fds8970}
}

@article{fds8973,
   Author = {Paul S Aspinwall},
   Title = {M-Theory Versus F-Theory Pictures of the Heterotic
             String},
   Journal = {Adv. Theo. Math. Phys. 1 (1997) 127-147,
             hep-th/9707014.},
   Key = {fds8973}
}

@article{fds8954,
   Author = {Paul S Aspinwall and D.R. Morrison},
   Title = {String Theory on K3 Surfaces},
   Journal = {in B. Greene and S.T. Yau, editors, "Mirror Symmetry II",
             pages 703-716, International Press, 1996,
             hep-th/9404151.},
   Key = {fds8954}
}

@article{fds8955,
   Author = {Paul S Aspinwall},
   Title = {Resolution of Orbifold Singularities in String
             Theory},
   Journal = {in B. Greene and S.T. Yau, editors, "Mirror Symmetry II",
             pages 355-426, International Press, 1996,
             hep-th/9403123.},
   Key = {fds8955}
}

@article{fds8957,
   Author = {Paul S Aspinwall and B.R. Greene and D.R. Morrison},
   Title = {Spacetime Topology Change: The Physics of Calabi-Yau Moduli
             Space},
   Journal = {in M.B. Halpern et al., editors, "Strings '93", pages
             241-262, World Scientific, 1995, hep-th/9311186.},
   Key = {fds8957}
}

@article{fds8958,
   Author = {Paul S Aspinwall},
   Title = {The Moduli Space of N = 2 Superconformal Field
             Theories},
   Journal = {in E. Gava et al., editors, "1994 Summer School in High
             Engergy Physics and Cosmology" pages 352-401, World
             Scientific, 1995, hep-th/9412115.},
   Key = {fds8958}
}