Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

TL;DR

This paper introduces gauge equivariant diffusion models using L-CNNs to accurately simulate non-Abelian lattice gauge theories, demonstrating strong generalization and efficiency in complex physics computations.

Contribution

The work presents a novel gauge equivariant diffusion framework with L-CNNs for non-Abelian lattice gauge theories, achieving accurate modeling from limited training data.

Findings

Models generalize well to larger lattices and couplings

High accuracy in Wilson loop and topological susceptibility calculations

Moderate acceptance rates maintained during simulations

Abstract

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.