Publications of Paul S. Aspinwall :recent first combined listing:
%% 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{fds243301,
Author = {Aspinwall, PS and Melnikov, IV and Ronen Plesser,
M},
Title = {(0,2) elephants},
Journal = {Journal of High Energy Physics},
Volume = {2012},
Number = {1},
Pages = {060},
Publisher = {Springer Nature},
Year = {2012},
Month = {February},
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{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},
Publisher = {Springer Nature},
Year = {1990},
Month = {March},
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}
}
@article{fds303518,
Author = {Aspinwall, PS},
Title = {A McKay-like correspondence for (0, 2)-deformations},
Journal = {Advances in Theoretical and Mathematical
Physics},
Volume = {18},
Number = {4},
Pages = {761-797},
Publisher = {International Press of Boston},
Year = {2014},
Month = {January},
url = {http://arxiv.org/abs/1110.2524v3},
Abstract = {We present a local computation of deformations of the
tangent bundle for a resolved orbifold singularity Cd/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
C3/Z7 has a nontrivial superpotential and thus an obstructed
moduli space.},
Doi = {10.4310/ATMP.2014.v18.n4.a1},
Key = {fds303518}
}
@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 = {029-029},
Publisher = {Springer Nature},
Year = {2000},
Month = {January},
url = {http://dx.doi.org/10.1088/1126-6708/2000/12/029},
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.},
Doi = {10.1088/1126-6708/2000/12/029},
Key = {fds243290}
}
@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},
Month = {January},
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{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},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
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{fds243287,
Author = {Aspinwall, PS},
Title = {Aspects of the hypermultiplet moduli space in string
duality},
Journal = {Journal of High Energy Physics},
Volume = {2},
Number = {4},
Pages = {019-019},
Publisher = {Springer Nature},
Year = {1998},
Month = {January},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/1998/04/019},
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.},
Doi = {10.1088/1126-6708/1998/04/019},
Key = {fds243287}
}
@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 = {034-034},
Publisher = {Springer Nature},
Year = {2007},
Month = {July},
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{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, Section B},
Volume = {416},
Number = {2},
Pages = {414-480},
Publisher = {Elsevier BV},
Year = {1994},
Month = {March},
url = {http://dx.doi.org/10.1016/0550-3213(94)90321-2},
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 Kähler sector of
the moduli space of such Calabi-Yau conformal theories
admits a decomposition into adjacent domains some of which
correspond to the (complexified) Kähler 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 Kähler 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 Kähler 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. © 1994.},
Doi = {10.1016/0550-3213(94)90321-2},
Key = {fds243273}
}
@article{fds303516,
Author = {Addington, N and Aspinwall, PS},
Title = {Categories of massless D-branes and del Pezzo
surfaces},
Journal = {Journal of High Energy Physics},
Volume = {2013},
Number = {7},
Publisher = {Springer Nature},
Year = {2013},
Month = {August},
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 Kähler 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 P 3, the category of
"Q-massless" objects is a "fractional Calabi-Yau" category
of graded matrix factorizations. © 2013 SISSA, Trieste,
Italy.},
Doi = {10.1007/JHEP07(2013)176},
Key = {fds303516}
}
@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},
Publisher = {Elsevier BV},
Year = {1994},
Month = {August},
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{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{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},
Publisher = {Springer Nature},
Year = {2006},
Month = {May},
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}
}
@booklet{Aspinwall90,
Author = {Aspinwall, PS and Lütken, CA and Ross, GG},
Title = {Construction and couplings of mirror manifolds},
Journal = {Physics Letters B},
Volume = {241},
Number = {3},
Pages = {373-380},
Publisher = {Elsevier BV},
Year = {1990},
Month = {May},
url = {http://dx.doi.org/10.1016/0370-2693(90)91659-Y},
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. ©
1990.},
Doi = {10.1016/0370-2693(90)91659-Y},
Key = {Aspinwall90}
}
@article{fds243296,
Author = {Aspinwall, PS and Douglas, MR},
Title = {D-brane stability and monodromy},
Journal = {Journal of High Energy Physics},
Volume = {6},
Number = {5},
Pages = {739-773},
Publisher = {Springer Nature},
Year = {2002},
Month = {May},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/2002/05/031},
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.},
Doi = {10.1088/1126-6708/2002/05/031},
Key = {fds243296}
}
@article{fds337142,
Author = {Aspinwall, PS},
Title = {D-branes on Calabi-Yau manifolds},
Pages = {1-152},
Booktitle = {Progress in String Theory, TASI 2003 Lecture
Notes},
Publisher = {World Scientific},
Year = {2005},
Month = {January},
url = {http://dx.doi.org/10.1142/9789812775108_0001},
Doi = {10.1142/9789812775108_0001},
Key = {fds337142}
}
@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{fds243292,
Author = {Aspinwall, PS and Plesser, MR},
Title = {D-branes, discrete torsion and the McKay
correspondence},
Journal = {Journal of High Energy Physics},
Volume = {5},
Number = {2},
Pages = {XIX-25},
Year = {2001},
Month = {January},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/2001/02/009},
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.},
Doi = {10.1088/1126-6708/2001/02/009},
Key = {fds243292}
}
@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{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},
Publisher = {Springer Nature},
Year = {2010},
Month = {January},
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 ℙn 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{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{fds243294,
Author = {Aspinwall, PS and Lawrence, A},
Title = {Derived categories and zero-brane stability},
Journal = {Journal of High Energy Physics},
Volume = {5},
Number = {8},
Pages = {1-26},
Publisher = {Springer Nature},
Year = {2001},
Month = {January},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/2001/08/004},
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.},
Doi = {10.1088/1126-6708/2001/08/004},
Key = {fds243294}
}
@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{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},
Publisher = {Elsevier BV},
Year = {1996},
Month = {March},
url = {http://dx.doi.org/10.1016/0370-2693(96)00003-2},
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.},
Doi = {10.1016/0370-2693(96)00003-2},
Key = {fds243279}
}
@article{fds243277,
Author = {Aspinwall, PS},
Title = {Enhanced gauge symmetries and K3 surfaces},
Journal = {Physics Letters B},
Volume = {357},
Number = {3},
Pages = {329-334},
Publisher = {Elsevier BV},
Year = {1995},
Month = {September},
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{fds243265,
Author = {Aspinwall, PS},
Title = {Exoflops in two dimensions},
Journal = {Journal of High Energy Physics},
Volume = {2015},
Number = {7},
Publisher = {Springer Nature},
Year = {2015},
Month = {July},
url = {http://dx.doi.org/10.1007/JHEP07(2015)104},
Abstract = {Abstract: An exoflop occurs in the gauged linear σ-model by
varying the Kähler form so that a subspace appears to
shrink to a point and then reemerge “outside” the
original manifold. This occurs for K3 surfaces where a
rational curve is “flopped” from inside to outside the
K3 surface. We see that whether a rational curve contracts
to an orbifold phase or an exoflop depends on whether this
curve is a line or conic. We study how the D-brane category
of the smooth K3 surface is described by the exoflop and, in
particular, find the location of a massless D-brane in the
exoflop limit. We relate exoflops to noncommutative
resolutions.},
Doi = {10.1007/JHEP07(2015)104},
Key = {fds243265}
}
@article{fds303519,
Author = {Aspinwall, PS and Kallosh, R},
Title = {Fixing all moduli for M-theory on K3×K3},
Journal = {Journal of High Energy Physics},
Volume = {2005},
Number = {10},
Pages = {1-20},
Publisher = {Springer Nature},
Year = {2005},
Month = {October},
url = {http://arxiv.org/abs/hep-th/0506014v1},
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 = {fds303519}
}
@article{fds322464,
Author = {Aspinwall, PS and Plesser, MR},
Title = {General mirror pairs for gauged linear sigma
models},
Journal = {Journal of High Energy Physics},
Volume = {2015},
Number = {11},
Pages = {1-33},
Publisher = {Springer Nature},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.1007/JHEP11(2015)029},
Abstract = {Abstract: We carefully analyze the conditions for an abelian
gauged linear σ-model to exhibit nontrivial IR behavior
described by a nonsingular superconformal field theory
determining a superstring vacuum. This is done without
reference to a geometric phase, by associating singular
behavior to a noncompact space of (semi-)classical vacua. We
find that models determined by reflexive combinatorial data
are nonsingular for generic values of their parameters. This
condition has the pleasant feature that the mirror of a
nonsingular gauged linear σ-model is another such model,
but it is clearly too strong and we provide an example of a
non-reflexive mirror pair. We discuss a weaker condition
inspired by considering extremal transitions, which is also
mirror symmetric and which we conjecture to be sufficient.
We apply these ideas to extremal transitions and to
understanding the way in which both Berglund-Hübsch mirror
symmetry and the Vafa-Witten mirror orbifold with discrete
torsion can be seen as special cases of the general
combinatorial duality of gauged linear σ-models. In the
former case we encounter an example showing that our weaker
condition is still not necessary.},
Doi = {10.1007/JHEP11(2015)029},
Key = {fds322464}
}
@booklet{Aspinwall91a,
Author = {Aspinwall, PS and Lütken, CA},
Title = {Geometry of mirror manifolds},
Journal = {Nuclear Physics, Section B},
Volume = {353},
Number = {2},
Pages = {427-461},
Publisher = {Elsevier BV},
Year = {1991},
Month = {April},
url = {http://dx.doi.org/10.1016/0550-3213(91)90343-V},
Abstract = {We analyze the mirror manifold hypothesis in one and three
dimensions using the simplest available representations of
the N = 2 superconformal 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 superconformal
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. ©
1991.},
Doi = {10.1016/0550-3213(91)90343-V},
Key = {Aspinwall91a}
}
@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://dx.doi.org/10.1088/1126-6708/2000/04/025},
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.},
Doi = {10.1088/1126-6708/2000/04/025},
Key = {fds243291}
}
@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},
Publisher = {Elsevier BV},
Year = {1996},
Month = {August},
url = {http://dx.doi.org/10.1016/0370-2693(96)00551-5},
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.},
Doi = {10.1016/0370-2693(96)00551-5},
Key = {fds243282}
}
@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{fds243305,
Author = {Aspinwall, PS},
Title = {Landau-Ginzburg to Calabi-Yau dictionary for
D-branes},
Journal = {Journal of Mathematical Physics},
Volume = {48},
Number = {8},
Pages = {082304-082304},
Publisher = {AIP Publishing},
Year = {2007},
Month = {September},
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{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 = {95-126},
Year = {2000},
Month = {January},
ISSN = {1095-0761},
url = {http://dx.doi.org/10.4310/atmp.2000.v4.n1.a2},
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.},
Doi = {10.4310/atmp.2000.v4.n1.a2},
Key = {fds243288}
}
@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{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},
Publisher = {Springer Nature},
Year = {2005},
Month = {October},
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{fds243269,
Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
Title = {Measuring small distances in N = 2 sigma
models},
Journal = {Nuclear Physics, Section B},
Volume = {420},
Number = {1-2},
Pages = {184-242},
Publisher = {Elsevier BV},
Year = {1994},
Month = {May},
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{fds243271,
Author = {Aspinwall, PS},
Title = {Minimum distances in non-trivial string target
spaces},
Journal = {Nuclear Physics, Section B},
Volume = {431},
Number = {1-2},
Pages = {78-96},
Publisher = {Elsevier BV},
Year = {1994},
Month = {December},
url = {http://dx.doi.org/10.1016/0550-3213(94)90098-1},
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. © 1994.},
Doi = {10.1016/0550-3213(94)90098-1},
Key = {fds243271}
}
@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},
Publisher = {Elsevier BV},
Year = {1993},
Month = {April},
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}
}
@article{fds243284,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Non-simply-connected gauge groups and rational points on
elliptic curves},
Journal = {Journal of High Energy Physics},
Volume = {1998},
Number = {7},
Pages = {012-012},
Publisher = {Springer Nature},
Year = {1998},
Month = {January},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/1998/07/012},
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.},
Doi = {10.1088/1126-6708/1998/07/012},
Key = {fds243284}
}
@article{fds243275,
Author = {Aspinwall, PS and Greene, BR},
Title = {On the geometric interpretation of N = 2 superconformal
theories},
Journal = {Nuclear Physics, Section B},
Volume = {437},
Number = {1},
Pages = {205-227},
Publisher = {Elsevier BV},
Year = {1995},
Month = {March},
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{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},
Publisher = {Elsevier BV},
Year = {1996},
Month = {February},
url = {http://dx.doi.org/10.1016/0370-2693(95)01541-8},
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.},
Doi = {10.1016/0370-2693(95)01541-8},
Key = {fds243278}
}
@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},
Month = {July},
url = {http://dx.doi.org/10.1016/S0550-3213(97)00232-0},
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.},
Doi = {10.1016/S0550-3213(97)00232-0},
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},
Publisher = {Elsevier BV},
Year = {1997},
Month = {October},
url = {http://dx.doi.org/10.1016/S0550-3213(97)00516-6},
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.},
Doi = {10.1016/S0550-3213(97)00516-6},
Key = {fds243285}
}
@booklet{Aspinwall91,
Author = {Aspinwall, PS and Lütken, CA},
Title = {Quantum algebraic geometry of superstring
compactifications},
Journal = {Nuclear Physics, Section B},
Volume = {355},
Number = {2},
Pages = {482-510},
Publisher = {Elsevier BV},
Year = {1991},
Month = {May},
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{fds243302,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Quivers from Matrix Factorizations},
Journal = {Communications in Mathematical Physics},
Volume = {313},
Number = {3},
Pages = {607-633},
Publisher = {Springer Nature},
Year = {2012},
Month = {August},
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{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},
Publisher = {Elsevier BV},
Year = {2015},
Month = {February},
ISSN = {0393-0440},
url = {http://dx.doi.org/10.1016/j.geomphys.2014.09.012},
Abstract = {We compare the count of (0, 2)-deformation moduli fields for
N=. (2, 2) conformal field theories on orbifolds and
sigma-models on resolutions of the orbifold. The latter
involves counting deformations of the tangent sheaf. We see
there is generally a discrepancy which is expected to be
explained by worldsheet instanton corrections coming from
rational curves in the orbifold resolution. We analyze the
rational curves on the resolution to determine such
corrections and discover that irreducible toric rational
curves account for some, but not all, of the discrepancy. In
particular, this proves that there must be worldsheet
instanton corrections beyond those from smooth isolated
rational curves.},
Doi = {10.1016/j.geomphys.2014.09.012},
Key = {fds243266}
}
@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{fds243267,
Author = {Aspinwall, PS and Greene, BR and Kirklin, KH and Miron,
PJ},
Title = {Searching for three-generation Calabi-Yau
manifolds},
Journal = {Nuclear Physics, Section B},
Volume = {294},
Number = {C},
Pages = {193-222},
Year = {1987},
Month = {January},
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{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{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},
Publisher = {Springer New York},
Year = {2013},
Month = {November},
ISBN = {9781461452911},
url = {http://dx.doi.org/10.1007/978-1-4614-5292-8_2},
Abstract = {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{fds243293,
Author = {Aspinwall, PS},
Title = {Some navigation rules for D-brane monodromy},
Journal = {Journal of Mathematical Physics},
Volume = {42},
Number = {12},
Pages = {5534-5552},
Publisher = {AIP Publishing},
Year = {2001},
Month = {December},
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{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},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
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{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},
Publisher = {AIP Publishing},
Year = {1994},
Month = {January},
ISSN = {0022-2488},
url = {http://dx.doi.org/10.1063/1.530754},
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.},
Doi = {10.1063/1.530754},
Key = {fds243272}
}
@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{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},
Publisher = {Springer Nature},
Year = {1996},
Month = {May},
url = {http://dx.doi.org/10.1007/BF02104911},
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.},
Doi = {10.1007/BF02104911},
Key = {fds243283}
}
@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{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{fds243307,
Author = {Aspinwall, PS and Fidkowski, LM},
Title = {Superpotentials for quiver gauge theories},
Journal = {Journal of High Energy Physics},
Volume = {2006},
Number = {10},
Pages = {047-047},
Publisher = {Springer Nature},
Year = {2006},
Month = {October},
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{fds243289,
Author = {Aspinwall, PS and Plesser, MR},
Title = {T-duality can fail},
Journal = {Journal of High Energy Physics},
Volume = {3},
Number = {8},
Pages = {XI-18},
Year = {1999},
Month = {January},
ISSN = {1029-8479},
url = {http://dx.doi.org/10.1088/1126-6708/1999/08/001},
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.},
Doi = {10.1088/1126-6708/1999/08/001},
Key = {fds243289}
}
@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{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},
Publisher = {International Press of Boston},
Year = {1998},
Month = {January},
ISSN = {1095-0761},
url = {http://dx.doi.org/10.4310/ATMP.1998.v2.n5.a4},
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.},
Doi = {10.4310/ATMP.1998.v2.n5.a4},
Key = {fds243286}
}
@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{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}
}
@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{Aspinwall93,
Author = {ASPINWALL, PS and GREENE, BR and MORRISON, DR},
Title = {THE MONOMIAL-DIVISOR MIRROR MAP},
Journal = {DUKE MATHEMATICAL JOURNAL},
Volume = {72},
Number = {3},
Pages = {319-337},
Publisher = {DUKE UNIV PRESS},
Year = {1993},
Month = {December},
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{fds303517,
Author = {Aspinwal, PS and Gross, M},
Title = {The SO(32) heterotic string on a K3 surface},
Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and
High-Energy Physics},
Volume = {387},
Number = {4},
Pages = {735-742},
Publisher = {Elsevier BV},
Year = {1996},
Month = {October},
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{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},
Publisher = {International Press of Boston},
Year = {2009},
Month = {January},
ISSN = {1931-4523},
url = {http://dx.doi.org/10.4310/CNTP.2009.v3.n3.a1},
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.},
Doi = {10.4310/CNTP.2009.v3.n3.a1},
Key = {fds243304}
}
@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},
Publisher = {Springer Nature},
Year = {1993},
Month = {January},
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}
}
@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},
Publisher = {Elsevier BV},
Year = {1995},
Month = {July},
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}
}
%% Preprints
@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{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{fds166462,
Author = {P.S. Aspinwall},
Title = {Probing Geometry with Stability Conditions},
Year = {2009},
Month = {May},
url = {http://arxiv.org/abs/0905.3137},
Key = {fds166462}
}