Related papers: Relevant Deformations, Brane Brick Models and Tria…
The gauge theory on a set of D3-branes at a toric Calabi-Yau singularity can be encoded in a tiling of the 2-torus denoted dimer diagram (or brane tiling). We use these techniques to describe the effect on the gauge theory of geometric…
In this thesis we elaborate on the three subjects of the title. We first show that supertubes exist and still preserve some supersymmetry in a large variety of curved backgrounds. Within the AdS/CFT correspondence we study the supersymmetry…
We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface $\Sigma_g$, with an arbitrary partial topological twist for the global $U(1)$ symmetries.…
Reflexive polygons have attracted great interest both in mathematics and in physics. This paper discusses a new aspect of the existing study in the context of quiver gauge theories. These theories are 4d supersymmetric worldvolume theories…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P^1's. As…
While Calabi-Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader perspective. With even the question of finiteness…
We study D1-branes on the fourfold $\C^4/(\Z_2\times\Z_2\times\Z_2)$, in the presence of discrete torsion. Discrete torsion is incorporated in the gauge theory of the D1-branes by considering a projective representation of the finite group…
In the context of string dualities, fibration structures of Calabi-Yau manifolds play a prominent role. In particular, elliptic and K3 fibered Calabi-Yau fourfolds are important for dualities between string compactifications with four flat…
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…
We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the…
In this review article we study type IIB superstring compactifications in the presence of space-time filling D-branes while preserving N=1 supersymmetry in the effective four-dimensional theory. This amount of unbroken supersymmetry and the…
We study open B-model representing D-branes on 2-cycles of local Calabi--Yau geometries. To this end we work out a reduction technique linking D-branes partition functions and multi-matrix models in the case of conifold geometries so that…
We construct a fully interacting holomorphic/topological theory in eleven dimensions that is defined on products of Calabi-Yau fivefolds with real one-manifolds. The theory describes a particular deformation of the cotangent bundle to the…
This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime…
In the first part of the talk, we discuss non-geometric twists and shifts and briefly review asymmetric orbifolds and free fermion constructions. These allow us to build Type IIB models with N = 1_L + 1_R and N = 1_L + 0_R models having few…
Three-branes at a given toric Calabi-Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find…
A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This approach is informed by homological mirror symmetry, derived…
Type II string theory compactified on a Calabi-Yau manifold, with a singularity modeled by a hypersurface in an orbifold, is considered. In the limit of vanishing string coupling, one expects a non gravitational theory concentrated at the…
We present general formulae for the TsT transformation (T-duality, shift, T-duality) of type II string backgrounds and open string boundary conditions. The TsT transformation provides a systematic procedure to find string theory duals of…