We develop a flow-based sampling algorithm for SU(N) lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an SU(N) variable (or on a U(N) variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single SU(N) variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.
@article{arxiv.2008.05456,
title = {Sampling using $SU(N)$ gauge equivariant flows},
author = {Denis Boyda and Gurtej Kanwar and Sébastien Racanière and Danilo Jimenez Rezende and Michael S. Albergo and Kyle Cranmer and Daniel C. Hackett and Phiala E. Shanahan},
journal= {arXiv preprint arXiv:2008.05456},
year = {2021}
}