Related papers: Brane Tilings and M2 Branes

We systematically study the master space of brane brick models that represent a large class of 2d (0,2) quiver gauge theories. These 2d (0,2) theories are worldvolume theories of D1-branes that probe singular toric Calabi-Yau 4-folds. The…

We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry…

We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to…

Given a brane tiling, that is a bipartite graph on a torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson-Thomas type…

We extend the study of relevant deformations connecting 2d (0,2) gauge theories on D1-branes probing toric Calabi-Yau 4-folds beyond pure mass deformations. The underlying geometry provides powerful insights when field-theoretic tools are…

Recent paper arXiv:1103.0553 studied the quiver gauge theories on coincident $M2$ branes on a singular toric Calabi-Yau 4-folds which are complex cone over toric Fano 3-folds. There are 18 toric Fano manifolds but only 14 toric Fano were…

We discuss the realization of $2d$ $(0,2)$ gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of $2d$ $(0,2)$…

We show that refined Chern-Simons theory and large N duality can be used to study the refined topological string with and without branes. We derive the refined topological vertex of hep-th/0701156 and hep-th/0502061 from a link invariant of…

We construct two-dimensional N=(2,2) supersymmetric gauge theories with orthogonal and symplectic groups using branes and orientifold planes in Type IIA string theory. A number of puzzles regarding the construction, including the effect of…

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT,…

A new way of computing scattering amplitudes in a certain very important QFT (N=4 SYM) has recently been developed, in which an algebraic structure called the positive Grassmannian plays a very important role. The mathematics of the…

Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. In this paper we study its commutative and non-commutative crepant resolutions. We give an explicit toric description of…

We study the recently proposed crystal model for three dimensional superconformal field theories arising from M2-branes probing toric Calabi-Yau four-fold singularities. We explain the algorithms mapping a toric Calabi-Yau to a crystal and…

We develop a framework to construct worldvolume gauge theories on D2-branes probing compound Du Val (cDV) Calabi-Yau threefold singularities. By viewing these singularities as ADE surface fibrations over the complex $w$-plane, we encode…

A number of N=2 gauge theories can be realized by brane configurations in Type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a…

We investigate features of duality in three dimensional N=2 Chern-Simons matter theories conjectured to describe M2 branes at toric Calabi Yau four-fold singularities. For 3D theories with non-chiral 4D parents we propone a Seiberg-like…

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to…

Motivated by the recent proposal of an N=8 supersymmetric action for multiple M2-branes, we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and the relation with Nambu-Poisson bracket. Some new…

We compute the elliptic genus of abelian 2d (0,2) gauge theories corresponding to brane brick models. These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity. We identify a match with the…

We derive the quiver gauge theory on the world-volume of D3-branes transverse to an L(a,b,c) singularity by computing the endomorphism algebra of a tilting object first constructed by Van den Bergh. The quiver gauge theory can be concisely…