Path integral contour deformations for observables in $SU(N)$ gauge theory

TL;DR

This paper introduces a family of contour deformations for $SU(N)$ lattice gauge theories that reduce sign and noise problems, using machine learning to optimize observables like Wilson loops, achieving significant variance reduction.

Contribution

It proposes a new class of contour deformations for $SU(N)$ gauge theories and demonstrates their effectiveness in variance reduction through machine learning optimization.

Findings

Achieved up to 4 orders of magnitude variance reduction.

Applied to Wilson loops with up to 64 plaquettes.

Validated on 2D $SU(2)$ and $SU(3)$ gauge theories.

Abstract

Path integral contour deformations have been shown to mitigate sign and signal-to-noise problems associated with phase fluctuations in lattice field theories. We define a family of contour deformations applicable to $SU(N)$ lattice gauge theory that can reduce sign and signal-to-noise problems associated with complex actions and complex observables. For observables, these contours can be used to define deformed observables with identical expectation value but different variance. As a proof-of-principle, we apply machine learning techniques to optimize the deformed observables associated with Wilson loops in two dimensional $SU(2)$ and $SU(3)$ gauge theory. We study loops consisting of up to 64 plaquettes and achieve variance reduction of up to 4 orders of magnitude.