Normalizing flows for SU($N$) gauge theories employing singular value decomposition

TL;DR

This paper introduces a novel method using singular value decomposition within normalizing flows to generate gauge configurations in SU(N) gauge theories, demonstrating improved efficiency and gauge invariance.

Contribution

The paper develops a new gauge-invariant transformation technique using SVD for normalizing flows in SU(N) gauge theories, applied to SU(3) on a small lattice.

Findings

Effective gauge-equivariant transformations constructed

Improved efficiency over spectral flow of Wilson loops

Successful training of models for SU(3) Wilson action

Abstract

We present a progress report on the use of normalizing flows for generating gauge field configurations in pure SU(N) gauge theories. We discuss how the singular value decomposition can be used to construct gauge-invariant quantities, which serve as the building blocks for designing gauge-equivariant transformations of SU(N) gauge links. Using this novel approach, we build representative models for the SU(3) Wilson action on a \( 4^4 \) lattice with \( \beta = 1 \). We train these models and provide an analysis of their performance, highlighting the effectiveness of the new technique for gauge-invariant transformations. We also provide a comparison between the efficiency of the proposed algorithm and the spectral flow of Wilson loops.