Signal-to-noise improvement through neural network contour deformations for 3D $SU(2)$ lattice gauge theory

TL;DR

This paper introduces a neural network-based method for contour deformations in lattice gauge theories, significantly enhancing the signal-to-noise ratio of Wilson loop measurements in 3D $SU(2)$ gauge theory.

Contribution

It develops a gauge fixing and neural network approach for contour deformations, enabling effective application in higher dimensions and with various boundary conditions.

Findings

Signal-to-noise ratio improved by up to three orders of magnitude

Applicable to higher-dimensional theories with generic boundary conditions

Demonstrated effectiveness in 3D $SU(2)$ lattice gauge theory

Abstract

Complex contour deformations of the path integral have been demonstrated to significantly improve the signal-to-noise ratio of observables in previous studies of two-dimensional gauge theories with open boundary conditions. In this work, new developments based on gauge fixing and a neural network definition of the deformation are introduced, which enable an effective application to theories in higher dimensions and with generic boundary conditions. Improvements of the signal-to-noise ratio by up to three orders of magnitude for Wilson loop measurements are shown in $SU(2)$ lattice gauge theory in three spacetime dimensions.