Metaheuristic Generation of Brane Tilings
Yang-Hui He, Vishnu Jejjala, Tom\'as S. R. Silva

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 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 quantum fields, illustrating the potential of metaheuristic techniques as a valuable addition to the toolbox for constructing and analyzing gauge theories from brane tilings.
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Taxonomy
TopicsStructural Analysis and Optimization
