Related papers: N=1 Mirror Symmetry and Open/Closed String Duality

We use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds. For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations,…

We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with…

We consider world-sheet instanton effects in N=1 string orientifolds of noncompact toric Calabi-Yau threefolds. We show that unoriented closed string topological amplitudes can be exactly computed using localization techniques for…

We discuss the vacuum structure of type IIA/B Calabi-Yau string compactifications to four dimensions in the presence of n-form H-fluxes. These will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic points in the…

We discuss the precise relation of the open N=2 string to a self-dual Yang-Mills (SDYM) system in 2+2 dimensions. In particular, we review the description of the string target space action in terms of SDYM in a ``picture hyperspace''…

We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1…

For compact Calabi-Yau geometries with D5-branes we study N=1 effective superpotentials depending on both open- and closed-string fields. We develop methods to derive the open/closed Picard-Fuchs differential equations, which control…

The first part of this review tries to provide a self-contained view of supersymmetry breaking from the bottom-up perspective. We thus describe N=1 supersymmetry in four dimensions, the Standard Model and the MSSM, with emphasis on the…

In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the…

We study orbifold compactifications of F-theory which lead to $N=1$ supersymmetry in 6 and 4 spacetime dimensions. These are dual to specific orientifolds of M-theory, and in many cases to orientifolds of type IIB string theory. The…

We develop techniques to compute higher loop string amplitudes for twisted $N=2$ theories with $\hat c=3$ (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states,…

We study the hypermultiplet moduli space of the type II string compactified on a Calabi-Yau space $\bX$. We do this by using IIA/IIB duality in a compactification of the same theory on $\bX\times \bS ^1$ and by using recent results on three…

We propose a construction of string cohomology spaces for Calabi-Yau hypersurfaces that arise in Batyrev's mirror symmetry construction. The spaces are defined explicitly in terms of the corresponding reflexive polyhedra in a…

We study quantum effects in five dimensions in heterotic superstring theory compactified on K_3 x S_1 and analyze the conjecture that its dual effective theory is eleven-dimensional supergravity compactified on a Calabi-Yau threefold. This…

We interpret the A and B model topological strings on CP^{3|4} as equivalent to open N=2 string theory on spacetime with signature (2,2), when covariantized with respect to SO(2,2) and supersymmetrized a la Siegel. We propose that…

The overarching goal of this thesis was to develop categorical methods that connect enumerative geometry, as studied in mirror symmetry, with large $N$ gauge theories. In the first part, we established a relation between graph complexes,…

Using mirror symmetry, we show that Chern-Simons theory on certain manifolds such as lens spaces reduces to a novel class of Hermitian matrix models, where the measure is that of unitary matrix models. We show that this agrees with the more…

In Calabi--Yau compactifications of the heterotic string there exist quantities which are universal in the sense that they are present in every Calabi--Yau string vacuum. It is shown that such universal characteristics provide numerical…

We study normal functions capturing D-brane superpotentials on several one- and two-parameter Calabi-Yau hypersurfaces and complete intersections in weighted projective space. We calculate in the B-model and interpret the results using…

We study toroidal compactifications of string theories which include compactification of a timelike coordinate. Some new features in the theory of toroidal compactifications arise. Most notably, Narain moduli space does not exist as a…