Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory

TL;DR

This paper introduces a tensor network approach to study three-dimensional non-Abelian gauge theories, specifically SU(2), by representing the path integral as a tensor network and optimizing variational parameters.

Contribution

It develops a tensor renormalization group method with variational parameters for 3D non-Abelian gauge theories, a novel extension beyond 2D applications.

Findings

Free energy results match analytical predictions in weak coupling.

Method successfully captures strong coupling behavior.

First tensor network study of 3D non-Abelian gauge theory.

Abstract

We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We construct initial tensors with indices labelling these gauge field configurations. We perform the tensor renormalization group with the initial tensors and optimize the variational parameters. As a first step to the TRG study of non-Abelian gauge theory in more than two dimensions, we apply this method to three-dimensional pure SU(2) gauge theory. Our result for the free energy agrees with the analytical results in weak and strong coupling regimes.