Metaheuristic tilings

The combinatorics of dimer models on brane tilings describe a large class of four-dimensional =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, whose construction is beyond the computational power of current methods.