Paul Stephen Aspinwall

Journal Article Journal of High Energy Physics · November 1, 2015 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 phas ... Full text Cite

Exoflops in two dimensions

Journal Article Journal of High Energy Physics · July 31, 2015 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 insi ... Full text Cite

Rational curves and (0, 2)-deformations

Journal Article Journal of Geometry and Physics · February 1, 2015 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 discr ... Full text Cite

A McKay-like correspondence for (0, 2)-deformations

Journal Article Advances in Theoretical and Mathematical Physics · January 1, 2014 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-o ... Full text Cite

Some applications of commutative algebra to string theory

Chapter · November 1, 2013 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. ... Full text Cite

Categories of massless D-branes and del Pezzo surfaces

Journal Article Journal of High Energy Physics · August 19, 2013 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 ... Full text Cite

Quivers from Matrix Factorizations

Journal Article Communications in Mathematical Physics · August 1, 2012 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 ... Full text Cite

(0,2) elephants

Journal Article Journal of High Energy Physics · February 27, 2012 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 Calab ... Full text Cite

Decompactifications and massless D-branes in hybrid models

Journal Article Journal of High Energy Physics · January 1, 2010 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 ... Full text Cite

Topological D-branes and commutative algebra

Journal Article Communications in Number Theory and Physics · January 1, 2009 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 demonstr ... Full text Cite

Landau-Ginzburg to Calabi-Yau dictionary for D-branes

Journal Article Journal of Mathematical Physics · September 7, 2007 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-Gin ... Full text Cite

Black hole entropy, marginal stability and mirror symmetry

Journal Article Journal of High Energy Physics · July 1, 2007 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 ... Full text Cite

Superpotentials for quiver gauge theories

Journal Article Journal of High Energy Physics · October 1, 2006 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 r ... Full text Cite

Computation of superpotentials for D-branes

Journal Article Communications in Mathematical Physics · May 1, 2006 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 ∞-st ... Full text Cite

Massless D-branes on Calabi-Yau threefolds and monodromy

Journal Article Communications in Mathematical Physics · October 1, 2005 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 ... Full text Cite

Fixing all moduli for M-theory on K3×K3

Journal Article Journal of High Energy Physics · October 1, 2005 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 ... Full text Cite

D-branes on Calabi-Yau manifolds

Journal Article · January 1, 2005 Full text Cite

D-branes on vanishing del Pezzo surfaces

Journal Article Journal of High Energy Physics · December 1, 2004 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-br ... Full text Cite

The breakdown of topology at small scales

Journal Article Journal of High Energy Physics · July 1, 2004 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 app ... Full text Cite

D-branes on vanishing del Pezzo surfaces

Journal Article Journal of High Energy Physics · 2004 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-br ... Cite

The breakdown of topology at small scales

Journal Article Journal of High Energy Physics · 2004 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 app ... Cite

Solitons in Seiberg-Witten theory and D-branes in the derived category

Journal Article Journal of High Energy Physics · April 1, 2003 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 ... Full text Cite

A point's point of view of stringy geometry

Journal Article Journal of High Energy Physics · January 1, 2003 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 ... Full text Cite

Solitons in Seiberg-Witten theory and D-branes in the derived category

Journal Article Journal of High Energy Physics · 2003 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 ... Cite

A point's point of view of stringy geometry

Journal Article Journal of High Energy Physics · 2003 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 ... Cite

D-brane stability and monodromy

Journal Article Journal of High Energy Physics · May 1, 2002 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 quinti ... Full text Cite

Some navigation rules for D-brane monodromy

Journal Article Journal of Mathematical Physics · December 1, 2001 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 ... Full text Cite

D-branes, discrete torsion and the McKay correspondence

Journal Article Journal of High Energy Physics · January 1, 2001 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 "regul ... Full text Cite

Derived categories and zero-brane stability

Journal Article Journal of High Energy Physics · January 1, 2001 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 D ... Full text Cite

D-branes, discrete torsion and the McKay correspondence

Journal Article Journal of High Energy Physics · 2001 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 "regul ... Cite

Heterotic string corrections from the dual type-II string

Journal Article Journal of High Energy Physics · January 1, 2000 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 ... Full text Cite

Heterotic string corrections from the dual type-II string

Journal Article Journal of High Energy Physics · 2000 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 ... Cite

A note on the equivalence of Vafa's and Douglas's picture of discrete torsion

Journal Article Journal of High Energy Physics · January 1, 2000 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. ... Full text Cite

Lie groups, Calabi-Yau threefolds, and F-theory

Journal Article Advances in Theoretical and Mathematical Physics · January 1, 2000 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 b ... Full text Cite

Compactification, Geometry and Duality: N=2

Journal Article · December 31, 1999 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 ... Link to item Cite

T-duality can fail

Journal Article Journal of High Energy Physics · January 1, 1999 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 ... Full text Cite

T-duality can fail

Journal Article Journal of High Energy Physics · 1999 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 ... Cite

Aspects of the hypermultiplet moduli space in string duality

Journal Article Journal of High Energy Physics · January 1, 1998 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 th ... Full text Cite

The heterotic string, The tangent bundle and derived categories

Journal Article Advances in Theoretical and Mathematical Physics · January 1, 1998 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 ... Full text Cite

Non-simply-connected gauge groups and rational points on elliptic curves

Journal Article Journal of High Energy Physics · January 1, 1998 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 fibra ... Full text Cite

Point-like instantons on K3 orbifolds

Journal Article Nuclear Physics B · October 20, 1997 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 ... Full text Cite

Point-like instantons and the Spin(32)/ℤ2 heterotic string

Journal Article Nuclear Physics B · July 7, 1997 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 a ... Full text Cite

The SO(32) heterotic string on a K3 surface

Journal Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics · October 31, 1996 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 met ... Full text Cite

Heterotic-heterotic string duality and multiple K3 fibrations

Journal Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics · August 1, 1996 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 equivalen ... Full text Cite

Stable singularities in string theory

Journal Article Communications in Mathematical Physics · May 1, 1996 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 o ... Full text Cite

Enhanced gauge symmetries and Calabi-Yau threefolds

Journal Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics · March 28, 1996 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 understo ... Full text Cite

On the ubiquity of K3 fibrations in string duality

Journal Article Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics · February 29, 1996 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 manifo ... Full text Cite

An N = 2 dual pair and a phase transition

Journal Article Nuclear Physics B · January 29, 1996 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 ach ... Full text Cite

Some relationships between dualities in string theory

Journal Article Nuclear Physics B - Proceedings Supplements · January 1, 1996 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 dimensi ... Full text Cite

Enhanced gauge symmetries and K3 surfaces

Journal Article Physics Letters B · September 7, 1995 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 ... Full text Cite

U-duality and integral structures

Journal Article Physics Letters B · July 27, 1995 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 s ... Full text Cite

On the geometric interpretation of N = 2 superconformal theories

Journal Article Nuclear Physics, Section B · March 6, 1995 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 ge ... Full text Cite

Minimum distances in non-trivial string target spaces

Journal Article Nuclear Physics, Section B · December 5, 1994 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 s ... Full text Cite

Chiral rings do not suffice: N=(2,2) theories with nonzero fundamental group

Journal Article Physics Letters B · August 11, 1994 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 ambig ... Full text Cite

Measuring small distances in N = 2 sigma models

Journal Article Nuclear Physics, Section B · May 30, 1994 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 the ... Full text Cite

Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory

Journal Article Nuclear Physics, Section B · March 28, 1994 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 ... Full text Cite

Space-time topology change and stringy geometry a

Journal Article Journal of Mathematical Physics · January 1, 1994 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 ... Full text Cite

THE MONOMIAL-DIVISOR MIRROR MAP

Journal Article DUKE MATHEMATICAL JOURNAL · December 1, 1993 Link to item Cite

Multiple mirror manifolds and topology change in string theory

Journal Article Physics Letters B · April 15, 1993 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 smoot ... Full text Cite

The monomial-divisor mirror map

Journal Article International Mathematics Research Notices · January 1, 1993 Full text Cite

Topological field theory and rational curves

Journal Article Communications in Mathematical Physics · January 1, 1993 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 ... Full text Cite

Quantum algebraic geometry of superstring compactifications

Journal Article Nuclear Physics, Section B · May 20, 1991 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 o ... Full text Cite

Geometry of mirror manifolds

Journal Article Nuclear Physics, Section B · April 15, 1991 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 mirro ... Full text Cite

Construction and couplings of mirror manifolds

Journal Article Physics Letters B · May 17, 1990 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 ... Full text Cite

(2, 2)-Superconformal field theories near orbifold points

Journal Article Communications in Mathematical Physics · March 1, 1990 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 agre ... Full text Cite

Searching for three-generation Calabi-Yau manifolds

Journal Article Nuclear Physics, Section B · January 1, 1987 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 ... Full text Cite