%% Books @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} } %% Papers Published @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{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{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{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{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)/ℤ_{2}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} } @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} } @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{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} } %% Papers Accepted @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} } %% Preprints @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{fds166462, Author = {P.S. Aspinwall}, Title = {Probing Geometry with Stability Conditions}, Year = {2009}, Month = {May}, url = {http://arxiv.org/abs/0905.3137}, Key = {fds166462} } @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{fds43748, Author = {P.S. Aspinwall}, Title = {An Analysis of Fluxes by Duality}, Year = {2005}, url = {http://arxiv.org/abs/hep-th/0504036}, Key = {fds43748} }