%% 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 = {Journal of High Energy Physics},
Volume = {2015},
Number = {11},
Pages = {133},
Publisher = {Springer Nature},
Year = {2015},
Month = {November},
url = {http://dx.doi.org/10.1007/JHEP11(2015)029},
Abstract = {© 2015, The Author(s). Abstract: We carefully analyze the
conditions for an abelian gauged linear σmodel 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
σmodel is another such model, but it is clearly too strong
and we provide an example of a nonreflexive 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 BerglundHübsch mirror symmetry and the VafaWitten
mirror orbifold with discrete torsion can be seen as special
cases of the general combinatorial duality of gauged linear
σmodels. 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}
}
@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 = {© 2015, The Author(s). Abstract: An exoflop occurs in the
gauged linear σmodel 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
Dbrane category of the smooth K3 surface is described by
the exoflop and, in particular, find the location of a
massless Dbrane in the exoflop limit. We relate exoflops to
noncommutative resolutions.},
Doi = {10.1007/JHEP07(2015)104},
Key = {fds243265}
}
@article{fds243266,
Author = {Aspinwall, PS and Gaines, B},
Title = {Rational curves and (0, 2)deformations},
Journal = {Journal of Geometry and Physics},
Volume = {88},
Pages = {115},
Publisher = {Elsevier BV},
Year = {2015},
Month = {February},
ISSN = {03930440},
url = {http://dx.doi.org/10.1016/j.geomphys.2014.09.012},
Abstract = {© 2014 Elsevier B.V. We compare the count of (0,
2)deformation moduli fields for N=. (2, 2) conformal field
theories on orbifolds and sigmamodels 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{fds303518,
Author = {Aspinwall, PS},
Title = {A McKaylike correspondence for (0, 2)deformations},
Journal = {Advances in Theoretical and Mathematical
Physics},
Volume = {18},
Number = {4},
Pages = {761797},
Publisher = {International Press of Boston},
Year = {2014},
Month = {January},
url = {http://arxiv.org/abs/1110.2524v3},
Abstract = {© 2014 International Press. 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 McKaylike
correspondence is found predicting the dimension of the
space of firstorder deformations from simple calculations
involving the group. This is confirmed in two dimensions
using the KronheimerNakajima 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 GHilbert scheme is never
subject to such corrections, and show this is true in an
infinite number of cases. Amusingly, for threedimensional
examples where G is abelian, the moduli space is associated
to a quiver given by the toric fan of the blowup. 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{fds243264,
Author = {Aspinwall, PS},
Title = {Some applications of commutative algebra to string
theory},
Pages = {2556},
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 = {1461452910},
url = {http://dx.doi.org/10.1007/9781461452928_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 = {10.1007/9781461452928_2},
Key = {fds243264}
}
@article{fds303516,
Author = {Addington, N and Aspinwall, PS},
Title = {Categories of massless Dbranes 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 Dbrane,
we define a notion of "Qmasslessness" 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 CalabiYau threefolds are
contracted. For precisely the del Pezzo surfaces that can be
written as hypersurfaces in weighted P 3 , the category of
"Qmassless" objects is a "fractional CalabiYau" category
of graded matrix factorizations. © 2013 SISSA, Trieste,
Italy.},
Doi = {10.1007/JHEP07(2013)176},
Key = {fds303516}
}
@article{fds243302,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Quivers from Matrix Factorizations},
Journal = {Communications in Mathematical Physics},
Volume = {313},
Number = {3},
Pages = {607633},
Publisher = {Springer Nature},
Year = {2012},
Month = {August},
ISSN = {00103616},
url = {http://dx.doi.org/10.1007/s0022001215201},
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 Dbranes (i. e.,
quiver representations) on a resolution given in terms of
Grassmannians. As an example we analyze some nontoric
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 LandauGinzburg theories to the way
that matrix factorizations are used in this paper to perform
noncommutative resolutions. © 2012 SpringerVerlag.},
Doi = {10.1007/s0022001215201},
Key = {fds243302}
}
@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 = {11266708},
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 CalabiYau threefold with the
\standard embedding" in three distinct ways. In the large
radius limit of the threefold, these singlets count
deformations of the CalabiYau together with its tangent
bundle. In the \smallradius" limit we apply LandauGinzburg
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{fds212419,
Author = {P.S. Aspinwall and M.R. Plesser},
Title = {Elusive Worldsheet Instantons in Heterotic String
Compactifications},
Volume = {85},
Pages = {3352},
Booktitle = {Proceedings of Symposia in Pure Mathematics},
Year = {2012},
url = {http://arxiv.org/abs/1106.2998},
Key = {fds212419}
}
@article{fds243303,
Author = {Aspinwall, PS and Ronen Plesser and M},
Title = {Decompactifications and massless Dbranes in hybrid
models},
Journal = {Journal of High Energy Physics},
Volume = {2010},
Number = {7},
Pages = {078},
Publisher = {Springer Nature},
Year = {2010},
Month = {July},
ISSN = {11266708},
url = {http://dx.doi.org/10.1007/jhep07(2010)078},
Abstract = {A method of determining the mass spectrum of BPS Dbranes in
any phase limit of a gauged linear sigma model is
introduced. A ring associated to monodromy is defined and
one considers Ktheory to be a module over this ring. A
simple but interesting class of hybrid models with
LandauGinzburg fibres over ℙ n are analyzed using special
Kähler geometry and Dbrane 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
Dbranes. 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 Dbranes and commutative algebra},
Journal = {Communications in Number Theory and Physics},
Volume = {3},
Number = {3},
Pages = {445474},
Publisher = {International Press of Boston},
Year = {2009},
Month = {January},
ISSN = {19314523},
url = {http://dx.doi.org/10.4310/CNTP.2009.v3.n3.a1},
Abstract = {We show that questions concerning the topological Bmodel on
a CalabiYau manifold in the LandauGinzburg 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 Dbranes 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 Dbranes.},
Doi = {10.4310/CNTP.2009.v3.n3.a1},
Key = {fds243304}
}
@article{fds243305,
Author = {Aspinwall, PS},
Title = {LandauGinzburg to CalabiYau dictionary for
Dbranes},
Journal = {Journal of Mathematical Physics},
Volume = {48},
Number = {8},
Pages = {082304082304},
Publisher = {AIP Publishing},
Year = {2007},
Month = {September},
ISSN = {00222488},
url = {http://dx.doi.org/10.1063/1.2768185},
Abstract = {Based on the work by Orlov (eprint arXiv:math.AG0503632),
we give a precise recipe for mapping between Btype Dbranes
in a LandauGinzburg orbifold model (or Gepner model) and
the corresponding large radius CalabiYau manifold. The
Dbranes in LandauGinzburg theories correspond to matrix
factorizations and the Dbranes on the CalabiYau 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 = {034034},
Publisher = {Springer Nature},
Year = {2007},
Month = {July},
ISSN = {11266708},
url = {http://dx.doi.org/10.1088/11266708/2007/07/034},
Abstract = {We consider the superconformal quantum mechanics associated
to BPS black holes in type IIB CalabiYau compactifications.
This quantum mechanics describes the dynamics of Dbranes in
the nearhorizon 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 Tdualities: 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 ×
T2case may be studied precisely using the FourierMukai
transform. © SISSA 2007.},
Doi = {10.1088/11266708/2007/07/034},
Key = {fds243306}
}
@article{fds152802,
Author = {P.S. Aspinwall},
Title = {The LandauGinzburg to CalabiYau Dictionary for
DBranes},
Journal = {J.Math.Phys.},
Volume = {48},
Pages = {082304},
Year = {2007},
Key = {fds152802}
}
@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 = {047047},
Publisher = {Springer Nature},
Year = {2006},
Month = {October},
ISSN = {10298479},
url = {http://dx.doi.org/10.1088/11266708/2006/10/047},
Abstract = {We compute superpotentials for quiver gauge theories arising
from marginal DBrane decay on collapsed del Pezzo cycles S
in a CalabiYau 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 = {10.1088/11266708/2006/10/047},
Key = {fds243307}
}
@article{fds243308,
Author = {Aspinwall, PS and Katz, S},
Title = {Computation of superpotentials for Dbranes},
Journal = {Communications in Mathematical Physics},
Volume = {264},
Number = {1},
Pages = {227253},
Publisher = {Springer Nature},
Year = {2006},
Month = {May},
ISSN = {00103616},
url = {http://dx.doi.org/10.1007/s0022000615276},
Abstract = {We present a general method for the computation of
treelevel superpotentials for the worldvolume theory of
Btype Dbranes. This includes quiver gauge theories in the
case that the Dbrane 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 ChernSimons theory. As an example, we give a
more rigorous proof of previous results concerning 3branes
on certain singularities including conifolds. We also
provide a new example.},
Doi = {10.1007/s0022000615276},
Key = {fds243308}
}
@article{fds51429,
Author = {P.S. Aspinwall},
Title = {DBranes, PiStability and ThetaStability},
Volume = {401},
Series = {Contemporary Mathematics},
Booktitle = {Snowbird Lectures on String Geometry},
Publisher = {AMS},
Year = {2006},
url = {http://arxiv.org/abs/hepth/0407123},
Key = {fds51429}
}
@article{fds243309,
Author = {Aspinwall, PS and Horja, RP and Karp, RL},
Title = {Massless Dbranes on CalabiYau threefolds and
monodromy},
Journal = {Communications in Mathematical Physics},
Volume = {259},
Number = {1},
Pages = {4569},
Publisher = {Springer Nature},
Year = {2005},
Month = {October},
url = {http://dx.doi.org/10.1007/s0022000513786},
Abstract = {We analyze the link between the occurrence of massless
Btype Dbranes for specific values of moduli and monodromy
around such points in the moduli space. This allows us to
propose a classification of all massless Btype Dbranes at
any point in the moduli space of CalabiYau'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 Dbrane becomes massless to generate
monodromies around points where an infinite number become
massless. We discuss the various possibilities within the
classification. © SpringerVerlag 2005.},
Doi = {10.1007/s0022000513786},
Key = {fds243309}
}
@article{fds303519,
Author = {Aspinwall, PS and Kallosh, R},
Title = {Fixing all moduli for Mtheory on K3×K3},
Journal = {Journal of High Energy Physics},
Volume = {2005},
Number = {10},
Pages = {120},
Publisher = {Springer Nature},
Year = {2005},
Month = {October},
url = {http://arxiv.org/abs/hepth/0506014v1},
Abstract = {We analyze Mtheory compactified on K3 × K3 with fluxes
preserving half the supersymmetry and its Ftheory 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 = {10.1088/11266708/2005/10/001},
Key = {fds303519}
}
@article{fds337142,
Author = {Aspinwall, PS},
Title = {Dbranes on CalabiYau manifolds},
Pages = {1152},
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{fds243300,
Author = {Aspinwall, PS and Kallosh, R},
Title = {Fixing all moduli for Mtheory on K3×K3},
Journal = {Journal of High Energy Physics},
Number = {10},
Pages = {120},
Year = {2005},
url = {http://dx.doi.org/10.1088/11266708/2005/10/001},
Abstract = {We analyze Mtheory compactified on K3 × K3 with fluxes
preserving half the supersymmetry and its Ftheory 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 = {10.1088/11266708/2005/10/001},
Key = {fds243300}
}
@article{fds243298,
Author = {Aspinwall, PS},
Title = {The breakdown of topology at small scales},
Journal = {Journal of High Energy Physics},
Volume = {8},
Number = {7},
Pages = {453463},
Year = {2004},
url = {http://arxiv.org/abs/hepth/0312188v1},
Abstract = {We discuss how a topology (the Zariski topology) on a space
can appear to break down at small distances due to Dbrane
decay. The mechanism proposed coincides perfectly with the
phase picture of CalabiYau moduli spaces. The topology
breaks down as one approaches nongeometric phases. This
picture is not without its limitations, which are also
discussed. © SISSA/ISAS 2004.},
Doi = {10.1088/11266708/2004/07/021},
Key = {fds243298}
}
@article{fds243299,
Author = {Aspinwall, PS and Melnikov, IV},
Title = {Dbranes on vanishing del Pezzo surfaces},
Journal = {Journal of High Energy Physics},
Volume = {8},
Number = {12},
Pages = {901930},
Year = {2004},
url = {http://arxiv.org/abs/hepth/0405134v2},
Abstract = {We analyze in detail the case of a marginally stable DBrane
on a collapsed del Pezzo surface in a CalabiYau threefold
using the derived category of quiver representations and the
idea of aligned gradings. We show how the derived category
approach to Dbranes provides a straightforward 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 tachyoninducing 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 = {10.1088/11266708/2004/12/042},
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 = {1731},
Year = {2003},
url = {http://arxiv.org/abs/hepth/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 Dbranes is the
key tool. The case of a flop is analyzed and IIstability in
this context is tied in to some ideas of Bridgeland.
Monodromy associated to the flop is also computed via
IIstability and shown to be consistent with previous
conjectures. © SISSA/ISAS 2003.},
Doi = {10.1088/11266708/2003/01/002},
Key = {fds243295}
}
@article{fds243297,
Author = {Aspinwall, PS and Karp, RL},
Title = {Solitons in SeibergWitten theory and Dbranes in the
derived category},
Journal = {Journal of High Energy Physics},
Volume = {7},
Number = {4},
Pages = {11191137},
Year = {2003},
url = {http://arxiv.org/abs/hepth/0211121v1},
Abstract = {We analyze the "geometric engineering" limit of a type II
string on a suitable CalabiYau threefold to obtain an N = 2
pure SU(2) gauge theory. The derived category picture
together with IIstability of Bbranes 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 = {10.1088/11266708/2003/04/049},
Key = {fds243297}
}
@article{fds243296,
Author = {Aspinwall, PS and Douglas, MR},
Title = {Dbrane stability and monodromy},
Journal = {Journal of High Energy Physics},
Volume = {6},
Number = {5},
Pages = {739773},
Publisher = {Springer Nature},
Year = {2002},
Month = {May},
ISSN = {10298479},
url = {http://dx.doi.org/10.1088/11266708/2002/05/031},
Abstract = {We review the idea of IIstability for Btype Dbranes on a
CalabiYau 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 CalabiYau 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 = {10.1088/11266708/2002/05/031},
Key = {fds243296}
}
@article{fds243293,
Author = {Aspinwall, PS},
Title = {Some navigation rules for Dbrane monodromy},
Journal = {Journal of Mathematical Physics},
Volume = {42},
Number = {12},
Pages = {55345552},
Publisher = {AIP Publishing},
Year = {2001},
Month = {December},
url = {http://dx.doi.org/10.1063/1.1409963},
Abstract = {We explore some aspects of monodromies of Dbranes in the
Kähler moduli space of CalabiYau compactifications. Here a
Dbrane 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 0brane. © 2001
American Institute of Physics.},
Doi = {10.1063/1.1409963},
Key = {fds243293}
}
@article{fds243294,
Author = {Aspinwall, PS and Lawrence, A},
Title = {Derived categories and zerobrane stability},
Journal = {Journal of High Energy Physics},
Volume = {5},
Number = {8},
Pages = {126},
Publisher = {Springer Nature},
Year = {2001},
Month = {January},
ISSN = {10298479},
url = {http://dx.doi.org/10.1088/11266708/2001/08/004},
Abstract = {© 2018 Elsevier B.V., All rights reserved. We define a
particular class of topological field theories associated to
open strings and prove the resulting Dbranes 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 0brane on any
CalabiYau 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 CalabiYaus.},
Doi = {10.1088/11266708/2001/08/004},
Key = {fds243294}
}
@article{fds243292,
Author = {Aspinwall, PS and Plesser, MR},
Title = {Dbranes, discrete torsion and the McKay
correspondence},
Journal = {Journal of High Energy Physics},
Volume = {5},
Number = {2},
Pages = {XIX25},
Year = {2001},
ISSN = {10298479},
url = {http://arxiv.org/abs/hepth/0009042},
Abstract = {We analyze the Dbranes of a typeIIB 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 Ktheory and homology. We find that discrete torsion
and torsion in this stringy homology are closelyrelated
concepts but that they differ in general. Lastly we question
to what extent the D1 brane may be thought of as being dual
to a string.},
Key = {fds243292}
}
@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 = {029029},
Publisher = {Springer Nature},
Year = {2000},
Month = {December},
url = {http://dx.doi.org/10.1088/11266708/2000/12/029},
Abstract = {For a general nonabelian group action and an arbitrary
genus worldsheet we show that Vafa's old definition of
discrete torsion coincides with Douglas's Dbrane definition
of discrete torsion associated to projective
representations.},
Doi = {10.1088/11266708/2000/12/029},
Key = {fds243290}
}
@article{fds243288,
Author = {Aspinwall, PS and Katz, S and Morrison, DR},
Title = {Lie groups, CalabiYau threefolds, and Ftheory},
Journal = {Advances in Theoretical and Mathematical
Physics},
Volume = {4},
Number = {1},
Pages = {124},
Year = {2000},
Month = {January},
ISSN = {10950761},
url = {http://arxiv.org/abs/hepth/0002012},
Abstract = {The Ftheory vacuum constructed from an elliptic CalabiYau
threefold with section yields an effective sixdimensional
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 CalabiYau
threefold. (Similar statements hold for Mtheory and the
type IIA string compactified on the threefold, where there
is also a dependence on the expectation values of the
RamondRamond fields.) We describe general rules for
computing the hypermultiplet spectrum of any Ftheory
vacuum, including vacua with nonsimplylaced 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 2branes are allowed
to wrap certain 2cycles. We also review the peculiar
numerical predictions for the geometry of elliptic
CalabiYau threefolds with section which arise from anomaly
cancellation in six dimensions.},
Key = {fds243288}
}
@article{fds243291,
Author = {Aspinwall, PS and Plesser, MR},
Title = {Heterotic string corrections from the dual typeII
string},
Journal = {Journal of High Energy Physics},
Volume = {4},
Number = {4},
Pages = {XXXIV21},
Year = {2000},
url = {http://arxiv.org/abs/hepth/9910248},
Abstract = {We introduce a method of using the a dual typeIIA 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
typeIIB strings compactified on a CalabiYau 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 pointlike
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/hepth/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 CalabiYau 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
nonexistence of a universal hypermultiplet are
discussed.},
Key = {fds303521}
}
@article{fds243289,
Author = {Aspinwall, PS and Plesser, MR},
Title = {Tduality can fail},
Journal = {Journal of High Energy Physics},
Volume = {3},
Number = {8},
Pages = {XI18},
Year = {1999},
ISSN = {10298479},
url = {http://arxiv.org/abs/hepth/9905036},
Abstract = {We show that Tduality can be broken by nonperturbative
effects in string coupling. The Tduality in question is
that of the 2torus when the heterotic string is
compactified on K3xT2. This case is compared carefully to a
situation where Tduality appears to work. A holonomy
argument is presented to show that Tdualities (and general
Udualities) 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 2torus appears to be broken too.},
Key = {fds243289}
}
@article{fds243284,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Nonsimplyconnected gauge groups and rational points on
elliptic curves},
Journal = {Journal of High Energy Physics},
Volume = {1998},
Number = {7},
Pages = {012012},
Publisher = {Springer Nature},
Year = {1998},
Month = {December},
ISSN = {10298479},
url = {http://dx.doi.org/10.1088/11266708/1998/07/012},
Abstract = {We consider the Ftheory description of nonsimplyconnected
gauge groups appearing in the E8× E8heterotic 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
E8which are applicable in this context. We also study the
closelyrelated question of pointlike 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 E8gauge symmetry broken to SU(9)/ℤ3or (E6×
SU(3))/ℤ3by pointlike instantons with
ℤ3holonomy.},
Doi = {10.1088/11266708/1998/07/012},
Key = {fds243284}
}
@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 = {019019},
Publisher = {Springer Nature},
Year = {1998},
Month = {December},
ISSN = {10298479},
url = {http://dx.doi.org/10.1088/11266708/1998/04/019},
Abstract = {A type IIA string (or Ftheory) compactified on a CalabiYau
threefold is believed to be dual to a heterotic string on a
K3 surface times a 2torus (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 G2bundles on the K3 surface and the case of pointlike
instantons. We are lead to a rather beautiful identification
between the integral cohomology of the CalabiYau 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 = {10.1088/11266708/1998/04/019},
Key = {fds243287}
}
@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 = {10411074},
Publisher = {International Press of Boston},
Year = {1998},
Month = {January},
ISSN = {10950761},
url = {http://dx.doi.org/10.4310/ATMP.1998.v2.n5.a4},
Abstract = {We consider the compactification of the E8×E8heterotic
string on a K3 surface with "the spin connection embedded in
the gauge group" and the dual picture in the type IIA string
(or Ftheory) on a CalabiYau threefold X. It turns out that
the same X arises also as dual to a heterotic
compactification on 24 pointlike instantons. X is
necessarily singular, and we see that this singularity
allows the RamondRamond moduli on X to split into distinct
components, one containing the (dual of the heterotic)
tangent bundle, while another component contains the
pointlike 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 Tduality
to the heterotic string on a K3 surface. © 1998
International Press.},
Doi = {10.4310/ATMP.1998.v2.n5.a4},
Key = {fds243286}
}
@article{fds243285,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Pointlike instantons on K3 orbifolds},
Journal = {Nuclear Physics B},
Volume = {503},
Number = {3},
Pages = {533564},
Publisher = {Elsevier BV},
Year = {1997},
Month = {October},
url = {http://dx.doi.org/10.1016/S05503213(97)005166},
Abstract = {The map between the moduli space of Ftheory (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 nonperturbative physics of collections of
E8 or Spin(32)/ℤ2 pointlike instantons sitting at ADE
singularities on a K3 surface. © 1997 Elsevier Science
B.V.},
Doi = {10.1016/S05503213(97)005166},
Key = {fds243285}
}
@article{fds243281,
Author = {Aspinwall, PS},
Title = {Pointlike instantons and the Spin(32)/ℤ2
heterotic string},
Journal = {Nuclear Physics B},
Volume = {496},
Number = {12},
Pages = {149176},
Year = {1997},
Month = {July},
url = {http://dx.doi.org/10.1016/S05503213(97)002320},
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 pointlike instanton  one "simple type" as
discovered by Witten and a new type associated to the
"generalized second StiefelWhitney 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 pointlike instantons to
coalesce, large gauge groups (e.g., rank 128) with many
massless tensor supermultiplets result. The analysis is done
in terms of Ftheory. © 1997 Elsevier Science
B.V.},
Doi = {10.1016/S05503213(97)002320},
Key = {fds243281}
}
@article{fds303517,
Author = {Aspinwal, PS and Gross, M},
Title = {The SO(32) heterotic string on a K3 surface},
Journal = {Physics Letters B},
Volume = {387},
Number = {4},
Pages = {735742},
Publisher = {Elsevier BV},
Year = {1996},
Month = {October},
url = {http://arxiv.org/abs/hepth/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 Ftheory)
on an elliptically fibred CalabiYau 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 pointlike 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 = {10.1016/03702693(96)010957},
Key = {fds303517}
}
@article{fds243282,
Author = {Aspinwall, PS and Gross, M},
Title = {Heteroticheterotic string duality and multiple K3
fibrations},
Journal = {Physics Letters B},
Volume = {382},
Number = {12},
Pages = {8188},
Publisher = {Elsevier BV},
Year = {1996},
Month = {August},
url = {http://dx.doi.org/10.1016/03702693(96)005515},
Abstract = {A type IIA string compactified on a CalabiYau manifold
which admits a K3 fibration is believed to be equivalent to
a heterotic string in four dimensions. We study cases where
a CalabiYau 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 CalabiYau manifold
which admits an infinite number of K3 fibrations leading to
infinite set of equivalent heterotic strings.},
Doi = {10.1016/03702693(96)005515},
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 = {115134},
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
nonlinear σmodel. 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{fds243279,
Author = {Aspinwall, PS},
Title = {Enhanced gauge symmetries and CalabiYau
threefolds},
Journal = {Physics Letters B},
Volume = {371},
Number = {34},
Pages = {231237},
Publisher = {Elsevier BV},
Year = {1996},
Month = {March},
url = {http://dx.doi.org/10.1016/03702693(96)000032},
Abstract = {We consider the general case of a type IIA string
compactified on a CalabiYau 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 stringstring
duality in six dimensions. We illustrate this with some
examples.},
Doi = {10.1016/03702693(96)000032},
Key = {fds243279}
}
@article{fds243278,
Author = {Aspinwall, PS and Louis, J},
Title = {On the ubiquity of K3 fibrations in string
duality},
Journal = {Physics Letters B},
Volume = {369},
Number = {34},
Pages = {233242},
Publisher = {Elsevier BV},
Year = {1996},
Month = {February},
url = {http://dx.doi.org/10.1016/03702693(95)015418},
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 CalabiYau 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 = {10.1016/03702693(95)015418},
Key = {fds243278}
}
@article{fds243276,
Author = {Aspinwall, PS},
Title = {An N = 2 dual pair and a phase transition},
Journal = {Nuclear Physics B},
Volume = {460},
Number = {1},
Pages = {5776},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.1016/05503213(95)006117},
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 nonperturbatively 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 = {10.1016/05503213(95)006117},
Key = {fds243276}
}
@article{fds243280,
Author = {Aspinwall, PS},
Title = {Some relationships between dualities in string
theory},
Journal = {Nuclear Physics B Proceedings Supplements},
Volume = {46},
Number = {13},
Pages = {3038},
Publisher = {Elsevier BV},
Year = {1996},
Month = {January},
url = {http://dx.doi.org/10.1016/09205632(96)000047},
Abstract = {Some relationships between string theories and
elevendimensional 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 elevendimensional supergravity and the
heterotic strings in ten dimensions.},
Doi = {10.1016/09205632(96)000047},
Key = {fds243280}
}
@article{fds243277,
Author = {Aspinwall, PS},
Title = {Enhanced gauge symmetries and K3 surfaces},
Journal = {Physics Letters B},
Volume = {357},
Number = {3},
Pages = {329334},
Publisher = {Elsevier BV},
Year = {1995},
Month = {September},
ISSN = {03702693},
url = {http://dx.doi.org/10.1016/03702693(95)00957M},
Abstract = {Stringstring duality dictates that type IIA strings
compactified on a K3 surface acquire nonabelian 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 "Bfield" 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 = {10.1016/03702693(95)00957M},
Key = {fds243277}
}
@article{fds243274,
Author = {Aspinwall, PS and Morrison, DR},
Title = {Uduality and integral structures},
Journal = {Physics Letters B},
Volume = {355},
Number = {12},
Pages = {141149},
Publisher = {Elsevier BV},
Year = {1995},
Month = {July},
ISSN = {03702693},
url = {http://dx.doi.org/10.1016/03702693(95)007457},
Abstract = {We analyze the Uduality 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 elevendimensional
supergravity, allowing all these theories to be directly
related to each other. The integral structure which appears
in the RamondRamond sector of the type II superstring is
related to the quantum cohomology of general CalabiYau
threefolds which allows the moduli space of type II
superstring compactifications on CalabiYau manifolds to be
analyzed. © 1995.},
Doi = {10.1016/03702693(95)007457},
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 = {205227},
Publisher = {Elsevier BV},
Year = {1995},
Month = {March},
ISSN = {05503213},
url = {http://dx.doi.org/10.1016/05503213(94)00571U},
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
CalabiYau 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 = {10.1016/05503213(94)00571U},
Key = {fds243275}
}
@article{fds243271,
Author = {Aspinwall, PS},
Title = {Minimum distances in nontrivial string target
spaces},
Journal = {Nuclear Physics B},
Volume = {431},
Number = {12},
Pages = {7896},
Publisher = {Elsevier BV},
Year = {1994},
Month = {December},
url = {http://dx.doi.org/10.1016/05503213(94)900981},
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 blownup quotient singularity
within a CalabiYau 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 = {10.1016/05503213(94)900981},
Key = {fds243271}
}
@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 = {12},
Pages = {7986},
Publisher = {Elsevier BV},
Year = {1994},
Month = {August},
ISSN = {03702693},
url = {http://dx.doi.org/10.1016/03702693(94)905940},
Abstract = {The Kähler moduli space of a particular
nonsimplyconnected CalabiYau 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 Amodel and Bmodel language. It also provides
an apparent counterexample to the global Torelli problem for
CalabiYau threefolds. © 1994.},
Doi = {10.1016/03702693(94)905940},
Key = {fds243270}
}
@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 = {12},
Pages = {184242},
Publisher = {Elsevier BV},
Year = {1994},
Month = {May},
ISSN = {05503213},
url = {http://dx.doi.org/10.1016/05503213(94)903794},
Abstract = {We analyze global aspects of the moduli space of Kähler
forms for N = (2,2) conformal σmodels. 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 CalabiYau 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 = {10.1016/05503213(94)903794},
Key = {fds243269}
}
@article{fds243273,
Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
Title = {CalabiYau moduli space, mirror manifolds and spacetime
topology change in string theory},
Journal = {Nuclear Physics B},
Volume = {416},
Number = {2},
Pages = {414480},
Publisher = {Elsevier BV},
Year = {1994},
Month = {March},
url = {http://dx.doi.org/10.1016/05503213(94)903212},
Abstract = {We analyze the moduli spaces of CalabiYau threefolds and
their associated conformally invariant nonlinear σmodels
and show that they are described by an unexpectedly rich
geometrical structure. Specifically, the Kähler sector of
the moduli space of such CalabiYau 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 CalabiYau
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 CalabiYau spacethe 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 CalabiYau 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 = {10.1016/05503213(94)903212},
Key = {fds243273}
}
@article{fds243272,
Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
Title = {Spacetime topology change and stringy geometry
a},
Journal = {Journal of Mathematical Physics},
Volume = {35},
Number = {10},
Pages = {53215337},
Publisher = {AIP Publishing},
Year = {1994},
Month = {January},
ISSN = {00222488},
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}
}
@booklet{Aspinwall93,
Author = {Aspinwall, PS and Greene, BR and Morrison, DR},
Title = {The MonomialDivisor Mirror Map},
Journal = {Internat. Math. Res. Notices (1993), 319337},
Volume = {72},
Number = {3},
Pages = {319  337},
Year = {1993},
Month = {September},
url = {http://arxiv.org/abs/alggeom/9309007v1},
Abstract = {For each family of CalabiYau hypersurfaces in toric
varieties, Batyrev has proposed a possible mirror partner
(which is also a family of CalabiYau 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 monomialdivisor 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 CalabiYau 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 CalabiYau 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}
}
@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 = {34},
Pages = {249259},
Publisher = {Elsevier BV},
Year = {1993},
Month = {April},
ISSN = {03702693},
url = {http://dx.doi.org/10.1016/03702693(93)91428P},
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 CalabiYau 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 = {10.1016/03702693(93)91428P},
Key = {Aspinwall93}
}
@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 = {245262},
Publisher = {Springer Nature},
Year = {1993},
Month = {January},
ISSN = {00103616},
url = {http://dx.doi.org/10.1007/BF02096768},
Abstract = {We analyze the quantum field theory corresponding to a
string propagating on a CalabiYau threefold. This theory
naturally leads to the consideration of Witten's topological
nonlinear σmodel and the structure of rational curves on
the CalabiYau manifold. We study in detail the case of the
worldsheet 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
SpringerVerlag.},
Doi = {10.1007/BF02096768},
Key = {Aspinwall93a}
}
@article{fds322465,
Author = {Aspinwall, PS and Morrison, DR and Greene, BR},
Title = {The monomialdivisor mirror map},
Journal = {International Mathematics Research Notices},
Volume = {1993},
Number = {12},
Pages = {319337},
Year = {1993},
Month = {January},
url = {http://dx.doi.org/10.1155/S1073792893000376},
Doi = {10.1155/S1073792893000376},
Key = {fds322465}
}
@booklet{Aspinwall91,
Author = {Aspinwall, PS and Lütken, CA},
Title = {Quantum algebraic geometry of superstring
compactifications},
Journal = {Nuclear Physics B},
Volume = {355},
Number = {2},
Pages = {482510},
Publisher = {Elsevier BV},
Year = {1991},
Month = {May},
ISSN = {05503213},
url = {http://dx.doi.org/10.1016/05503213(91)90123F},
Abstract = {We investigate the algebraogeometric structure which is
inherent in 2dimensional conformally invariant quantum
field theories with N=2 supersymmetry, and its relation to
the CalabiYau manifolds which appear in the socalled
"large radius limit". Based on a careful comparison of the
Kähler cone of CalabiYau 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(b3, 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 = {10.1016/05503213(91)90123F},
Key = {Aspinwall91}
}
@booklet{Aspinwall91a,
Author = {Aspinwall, PS and Lütken, CA},
Title = {Geometry of mirror manifolds},
Journal = {Nuclear Physics B},
Volume = {353},
Number = {2},
Pages = {427461},
Publisher = {Elsevier BV},
Year = {1991},
Month = {April},
url = {http://dx.doi.org/10.1016/05503213(91)90343V},
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 TianYau 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 = {10.1016/05503213(91)90343V},
Key = {Aspinwall91a}
}
@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 = {373380},
Publisher = {Elsevier BV},
Year = {1990},
Month = {May},
url = {http://dx.doi.org/10.1016/03702693(90)91659Y},
Abstract = {We present an analysis of the conjectured existence of
CalabiYau "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 largeradius 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 = {10.1016/03702693(90)91659Y},
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 = {593611},
Publisher = {Springer Nature},
Year = {1990},
Month = {March},
ISSN = {00103616},
url = {http://dx.doi.org/10.1007/BF02096875},
Abstract = {A thorough analysis of the "blowingup" 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 CalabiYau compactification
are not immediately in agreement. A solution to this
apparent inconsistency is offered which leads to the
possibility of differentiably distinct CalabiYau manifolds
giving isomorphic physics. © 1990 SpringerVerlag.},
Doi = {10.1007/BF02096875},
Key = {fds243268}
}
@article{fds243267,
Author = {Aspinwall, PS and Greene, BR and Kirklin, KH and Miron,
PJ},
Title = {Searching for threegeneration CalabiYau
manifolds},
Journal = {Nuclear Physics B},
Volume = {294},
Number = {C},
Pages = {193222},
Year = {1987},
Month = {January},
ISSN = {05503213},
url = {http://dx.doi.org/10.1016/05503213(87)905797},
Abstract = {All possible CalabiYau manifolds realisable as complete
intersections and quotients of complete intersections by
projectivelyinherited symmetries are considered. We develop
a stringent set of criteria with which to exhaustively
search this huge class for threegeneration manifolds. We
find only one manifold meeting our conditions  namely the
first manifold discovered by Yau. In addition it is shown
that all known threegeneration CalabiYau manifolds are
either diffeomorphic to this one example or illdefined. ©
1987.},
Doi = {10.1016/05503213(87)905797},
Key = {fds243267}
}
@booklet{Aspinwall87,
Author = {Aspinwall, PS and Greene, BR and Kirklin, KH and Miron,
PJ},
Title = {Searching for threegeneration CalabiYau
manifolds},
Journal = {Nuclear Physics B},
Volume = {294},
Number = {1},
Pages = {193222},
Publisher = {Elsevier BV},
Year = {1987},
Month = {January},
ISSN = {05503213},
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 = {10.1016/05503213(87)905797},
Key = {Aspinwall87}
}
@article{fds10130,
Author = {Paul S. Aspinwall and Albion Lawrence},
Title = {Derived Categories and 0Brane Stability},
Journal = {J. High Energy Phys. 08 (2001) 004},
url = {http://arxiv.org/abs/hepth/0104147},
Key = {fds10130}
}
@article{fds8976,
Author = {Paul S Aspinwall},
Title = {String Theory and Duality},
Journal = {Doc. Math. J. DMV Extra Volume ICM II (1998)
229238.},
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 421540, World Scientific,
1997.},
url = {http://arxiv.org/abs/hepth/9611137},
Key = {fds8970}
}
@article{fds8973,
Author = {Paul S Aspinwall},
Title = {MTheory Versus FTheory Pictures of the Heterotic
String},
Journal = {Adv. Theo. Math. Phys. 1 (1997) 127147,
hepth/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 703716, International Press, 1996,
hepth/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 355426, International Press, 1996,
hepth/9403123.},
Key = {fds8955}
}
@article{fds8957,
Author = {Paul S Aspinwall and B.R. Greene and D.R. Morrison},
Title = {Spacetime Topology Change: The Physics of CalabiYau Moduli
Space},
Journal = {in M.B. Halpern et al., editors, "Strings '93", pages
241262, World Scientific, 1995, hepth/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 352401, World
Scientific, 1995, hepth/9412115.},
Key = {fds8958}
}
%% Preprints
@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 = {DBranes on Toric CalabiYau 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/hepth/0504036},
Key = {fds43748}
}
