Neural Network Gauge Field Transformation for 4D SU(3) gauge fields

TL;DR

This paper introduces neural network-based gauge field transformations that are gauge covariant, scalable, and applicable to 4D SU(3) lattice gauge fields, with potential to improve Hybrid Monte Carlo methods.

Contribution

It develops a general neural network framework for gauge covariant transformations applicable to any Lie group, specifically demonstrating its use for 4D SU(3) lattice gauge fields.

Findings

Transformations preserve gauge covariance and invertibility.

Impact on HMC molecular dynamics demonstrated.

Scalability of the neural network approach discussed.

Abstract

We construct neural networks that work for any Lie group and maintain gauge covariance, enabling smooth, invertible gauge field transformations. We implement these transformations for 4D SU(3) lattice gauge fields and explore their use in HMC. We focus on developing loss functions and optimizing the transformations. We show the effects on HMC's molecular dynamics and discuss the scalability of the approach.