# Hodge gauge fixing in three dimensions

## TL;DR

This paper discusses a gauge fixing method for three-dimensional lattice gauge theories, focusing on diagonalizing SU(N) operators and addressing issues like monopoles and zero modes.

## Contribution

It presents an implementation and analysis of a gauge fixing algorithm based on diagonalizing SU(N) operators and separating physical and gauge parts of the link fields.

## Key findings

- Successful gauge fixing in three dimensions with addressed monopole issues
- Separation of physical gauge fields from pure gauge and lattice artifacts
- Insights into zero mode handling in lattice gauge fixing

## Abstract

A progress report on experiences with a gauge fixing method proposed in LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized at each site, followed by gauge fixing the diagonal (Cartan) part of the links to Coulomb gauge using the residual abelian freedom. The Cartan sector of the link field is separated into the physical gauge field $\alpha^{(f)}_\mu$ responsible for producing $f^{\rm Cartan}_{\mu\nu}$, the pure gauge part, lattice artifacts, and zero modes. The gauge transformation to the physical gauge field $\alpha^{(f)}_\mu$ is then constructed and performed. Compactness of the lattice fields entails issues related to monopoles and zero modes which are addressed.