Sampling using $SU(N)$ gauge equivariant flows

TL;DR

This paper introduces a gauge-invariant flow-based sampling algorithm for $SU(N)$ lattice gauge theories, enabling efficient and symmetry-respecting sampling of gauge variables, demonstrated on $SU(2)$ and $SU(3)$ in two dimensions.

Contribution

The authors develop a novel class of gauge-equivariant flows on $SU(N)$ variables, ensuring gauge invariance by construction, and apply it to lattice gauge theory sampling.

Findings

Successfully sampled $SU(2)$ and $SU(3)$ gauge theories in two dimensions.

Constructed gauge-equivariant flows respecting matrix conjugation symmetry.

Demonstrated gauge-invariant sampling without explicit gauge fixing.

Abstract

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.