Related papers: Modelling $A$-branes with foliations

The field content and interactions of almost all known gauge theories in AdS_5/CFT_4 can be expressed in terms of dimer models or bipartite graphs drawn on a torus. Associated with the fundamental cell is a complex structure parameter…

We present explicit methods for computing the discriminant curves and the associated Kodaira type fiber degeneracies of elliptically fibered Calabi-Yau threefolds. These methods are applied to a specific three-family, SU(5) grand unified…

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze…

We analyze B-type D-branes on noncompact toric Calabi--Yau spaces. A general program is presented to find a set of tilting line bundles that yields the associated quiver and its relations. In many cases, this set remains fixed as one moves…

In certain regions of the moduli space of K3 and Calabi-Yau manifolds, D-branes wrapped on non-supersymmetric cycles may give rise to stable configurations. We show that in the orbifold limit, some of these stable configurations can be…

We review free fermion, melting crystal and matrix model representations of wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both unrefined and refined BPS counting of closed BPS states involving D2 and D0-branes…

We describe eight-dimensional vacuum configurations with varying moduli consistent with the U-duality group $SL(2,Z) \times SL(3,Z)$. Focusing on the latter less-well understood SL(3,Z) properties, we construct a class of fivebrane…

We define an algebra on the space of BPS states in theories with extended supersymmetry. We show that the algebra of perturbative BPS states in toroidal compactification of the heterotic string is closely related to a generalized Kac-Moody…

We use wrapped D-brane probes to measure position dependent perturbations of compactification moduli. Due to the backreaction of the D-branes on the local geometry, we suspect that measuring the fluctuations of one modulus to high precision…

We study D-branes on smooth noncompact toric Calabi-Yau manifolds that are resolutions of abelian orbifold singularities. Such a space has a distinguished basis {S_i} for the compactly supported K-theory. Using local mirror symmetry we…

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…

We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric Calabi-Yau threefold, the D-branes wrapping holomorphic…

I point out that (BPS saturated) A-type D-branes in superstring compactifications on Calabi-Yau threefolds correspond to {\em graded} special Lagrangian submanifolds, a particular case of the graded Lagrangian submanifolds considered by M.…

We study open-closed orbifold Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric Deligne-Mumford (DM) stacks (with possibly non-trivial generic stabilizers and semi-projective coarse moduli spaces) relative to Lagrangian…

We study a flat connection defined on the open-closed deformation space of open string mirror symmetry for type II compactifications on Calabi-Yau threefolds with D-branes. We use flatness and integrability conditions to define…

This work discusses string compactifications on the torus with optional Z_4 x Z_4 or Z_2 x Z_2 orbifold action from the perspective of matrix factorizations. The method is brought to a level where model building on these backgrounds is…

In the search for a classification of BPS backgrounds with flux, we look at geometries that arise when M-branes wrap supersymmetric cycles in Calabi-Yau manifolds. We find constraints on the differential forms in the back-reacted manifolds…

The versal deformation of Stanley-Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and…

We consider M-theory compactification on Calabi-Yau threefolds. The recently discovered connection between the BPS states of wrapped M2 branes and the topological string amplitudes on the threefold is used both as a tool to compute…

The modified elliptic genus for an M5-brane wrapped on a four-cycle of a Calabi-Yau threefold encodes the degeneracies of an infinite set of BPS states in four dimensions. By holomorphy and modular invariance, it can be determined…