Journal ArticleJournal of High Energy Physics · March 1, 2025
The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be used to find param ...
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Journal Article · February 15, 2017
We analyze the locus, together with multiplicities, of "bad" conformal field
theories in the compactified moduli space of N=(2,2) superconformal field
theories in the context of the generalization of the Batyrev mirror
construction using the gauged linear ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleAdvances 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 ...
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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. ...
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Journal ArticleJournal 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 ...
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Journal ArticleCommunications 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleCommunications 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 i ...
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Journal ArticleCommunications 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
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Journal ArticleCommunications 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 ...
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Journal ArticleJournal 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 s ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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. ...
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Journal ArticleAdvances 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 ...
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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 ...
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Journal ArticleJournal 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-dual ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleAdvances 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 ...
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Journal ArticleJournal 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 corres ...
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Journal ArticleNuclear 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleCommunications 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleCommunications 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticleNuclear 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 ...
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Journal ArticlePhysics 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 h< ...
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Journal ArticleCommunications 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 compactific ...
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Journal ArticleNuclear 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 ...
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