Quivers, Tilings, Branes and Rhombi
Amihay Hanany, David Vegh

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.
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