Machine learning for four-dimensional SU(3) lattice gauge theories

TL;DR

This review discusses how machine learning techniques, including generative models and RG-based methods, are applied to improve sampling and analyze four-dimensional SU(3) lattice gauge theories, with promising results towards the continuum limit.

Contribution

It summarizes current machine learning approaches in lattice gauge theory, introduces a machine-learned fixed-point action, and presents scaling results for continuum extrapolation.

Findings

Scaling results for a machine-learned fixed-point action towards the continuum limit.

Observables based on gradient-flow scales free of lattice artefacts.

Quantities related to static potential and deconfinement transition.

Abstract

In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap\-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in four-dimensional SU(3) gauge theories. These include approaches based on generative machine-learning models such as (stochastic) normalizing flows and diffusion processes, and an approach based on renormalization group (RG) transformations, more specifically the machine learning of RG-improved gauge actions using gauge-equivariant convolutional neural networks. In particular, I present scaling results for a machine-learned fixed-point action in four-dimensional SU(3) gauge theory towards the continuum limit. The results include observables based on the classically perfect gradient-flow scales, which are free of tree-level lattice artefacts to all orders, and quantities related to the static potential and the deconfinement transition.