On Dimer Models and Closed String Theories

TL;DR

This paper explores the connection between dimer models and closed string theories, revealing how perfect matchings relate to twisted sector states and applying this to analyze unstable orbifolds of complex spaces.

Contribution

It introduces a novel link between dimer models and closed string theories on orbifolds, expanding the understanding of their interplay and applications.

Findings

Perfect matchings correspond to twisted sector states in closed string theories.

Dimer models relate to orbifold theories via twisted sector R charges.

Application to unstable orbifolds of ^2 demonstrates the formalism's utility.

Abstract

We study some aspects of the recently discovered connection between dimer models and D-brane gauge theories. We argue that dimer models are also naturally related to closed string theories on non compact orbifolds of $\BC^2$ and $\BC^3$, via their twisted sector R charges, and show that perfect matchings in dimer models correspond to twisted sector states in the closed string theory. We also use this formalism to study the combinatorics of some unstable orbifolds of $\BC^2$.