Dimer models and toric diagrams

TL;DR

This paper establishes a duality between quiver gauge theories and dimer models, linking combinatorics with gauge theory data through toric diagrams and multiplicities, offering new computational tools and insights.

Contribution

It introduces a duality connecting quiver gauge theories with dimer models via toric diagrams, providing formulas and algorithms for analyzing orbifolds and phase structures.

Findings

Multiplicities in toric diagrams can be computed from both gauge theories and dimer models and are consistent.

Dimer models yield a closed-form formula for orbifold multiplicities.

An algorithmic approach is developed for exploring quiver gauge theory phases.

Abstract

We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the linear sigma model construction of the toric space). These multiplicities may be computed from both sides and are found to agree in all known examples. The dimer models provide new insights into the quiver gauge theories: for example they provide a closed formula for the multiplicities of arbitrary orbifolds of a toric space, and allow a new algorithmic method for exploring the phase structure of the quiver gauge theory.