Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory
This work addresses computational challenges in lattice gauge theory for physics researchers, representing an incremental improvement with novel method application.
The authors tackled the problem of modeling non-Abelian lattice gauge theory physics by developing gauge equivariant diffusion models, achieving accurate generalization to larger inverse couplings and lattice sizes with negligible accuracy loss and moderately high acceptance rates.
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.