Related papers: Bipartita: Physics, Geometry & Number Theory
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…
We present bipartiteSUSY, a Mathematica package designed to perform calculations for physical theories based on bipartite graphs. In particular, the package can employ the recently developed arsenal of techniques surrounding on-shell…
We develop tools for determining the gauge theory resulting from a configuration of Type IIB D3-branes probing a non-compact, toric Calabi-Yau 3-fold, in the presence of additional flavor D7-branes with general embeddings. Two main…
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding this…
Ribbon graphs embedded on a Riemann surface provide a useful way to describe the double line Feynman diagrams of large N computations and a variety of other QFT correlator and scattering amplitude calculations, e.g in MHV rules for…
We review recent developments in the theory of brane tilings and four-dimensional N=1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical…
We review recent progress in Bipartite Field Theories. We cover topics such as their gauge dynamics, emergence of toric Calabi-Yau manifolds as master and moduli spaces, string theory embedding, relationships to on-shell diagrams,…
The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…
Each finite and connected bipartite graph induces a finite collection of non-isomorphic dessins d'enfants, that is, $2$-cell embeddings of it into some closed orientable surface. We describe an algorithm to compute all these dessins…
Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite…
The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…
Dessin d'Enfants on elliptic curves are a powerful way of encoding doubly-periodic brane tilings, and thus, of four-dimensional supersymmetric gauge theories whose vacuum moduli space is toric, providing an interesting interplay between…
We describe a simple algorithm that computes the recently discovered brane tilings for a given generic toric singular Calabi-Yau threefold. This therefore gives AdS/CFT dual quiver gauge theories for D3-branes probing the given non-compact…
We study pairs of 4d N=1 supersymmetric gauge theories that share the same vacuum moduli space and the same chiral field content, encoded by a common quiver, but differ in their superpotentials. These theories arise as worldvolume theories…
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite…
We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone,…
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 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…
Bipartite field theories (BFTs) are a new class of 4d N=1 quantum field theories defined by bipartite graphs on bordered Riemann surfaces. In this paper we derive, purely in terms of the gauge theory, the cluster transformations of face…
We study the algebraic structure of the mesonic moduli spaces of bipartite field theories by computing the Hilbert series. Bipartite field theories form a large family of 4d N=1 supersymmetric gauge theories that are defined by bipartite…