Quivers, Tilings, Branes and Rhombi

TL;DR

This paper presents a straightforward algorithm to compute brane tilings for toric Calabi-Yau threefolds, enabling direct derivation of superpotentials and R-charges in dual quiver gauge theories, and offers new insights into Seiberg duality.

Contribution

It introduces a simple algorithm for computing brane tilings directly from toric diagrams, solving a longstanding problem in the field.

Findings

Algorithm efficiently computes brane tilings from toric diagrams

Identifies R-charges as angles in brane tilings

Provides new perspective on Seiberg duality

Abstract

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 manifold. The algorithm solves a longstanding problem by computing superpotentials for these theories directly from the toric diagram of the singularity. We study the parameter space of a-maximization; this study is made possible by identifying the R-charges of bifundamental fields as angles in the brane tiling. We also study Seiberg duality from a new perspective.