Metaheuristic Generation of Brane Tilings

TL;DR

This paper presents a novel combinatorial optimization approach using simulated annealing to efficiently generate consistent brane tilings, which describe a broad class of gauge theories with toric moduli spaces.

Contribution

It introduces a metaheuristic method for constructing brane tilings, demonstrating its effectiveness by recovering known examples and creating a new tiling with 26 quantum fields.

Findings

Successfully recovers known brane tilings

Generates a new brane tiling with 26 quantum fields

Shows potential of metaheuristic techniques in gauge theory construction

Abstract

The combinatorics of dimer models on brane tilings describe a large class of four-dimensional $\mathcal{N}=1$ gauge theories that afford quiver descriptions and have toric moduli spaces. We introduce a combinatorial optimization method leveraging simulated annealing to explicitly construct geometrically consistent brane tilings, providing a proof of concept for efficient generation of gauge theories using metaheuristic techniques. The implementation of this idea recovers known examples and allows us to derive a new brane tiling with $26$ quantum fields, illustrating the potential of metaheuristic techniques as a valuable addition to the toolbox for constructing and analyzing gauge theories from brane tilings.