On the structure of quadrilateral brane tilings

TL;DR

This paper investigates the structure of quadrilateral brane tilings, providing a method to generate all such tilings and analyzing their impact on associated quiver gauge theories, superpotentials, and superconformal fixed points.

Contribution

It introduces a graph-theoretic method to generate quadrilateral brane tilings and examines their effects on gauge theories and dualities in string theory.

Findings

A systematic method to generate quadrilateral brane tilings.

Analysis of how tilings affect superpotentials and moduli spaces.

Insights into Seiberg duality within this class of tilings.

Abstract

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 tiling of the torus which encodes both the classical superpotential and gauge-matter couplings for the quiver gauge theory. We consider the class of tilings which contain only tiles bounded by exactly four edges and present a method for generating any tiling within this class by iterating combinations of certain graph-theoretic moves. In the context of D3-branes in IIB string theory, we consider the effect of these generating moves within the corresponding class of supersymmetric quiver gauge theories in four dimensions. Of particular interest are their effect on the superpotential, the vacuum moduli space and the conditions necessary for the theory to reach a superconformal fixed point in the infrared. We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.