# A Gauge-Fixing Action for Lattice Gauge Theories

## TL;DR

This paper introduces a new lattice gauge-fixing action that ensures a unique minimum and discusses its implications for the phase diagram, addressing challenges of gauge fixing in lattice gauge theories.

## Contribution

The paper proposes a gauge-fixing action for lattice gauge theories with a unique minimum, enhancing the understanding of gauge fixing on the lattice.

## Key findings

- The gauge-fixing action is proportional to the trace of the divergence squared.
- It has a unique absolute minimum at the identity configuration.
- The paper discusses phase diagram implications and the non-BRST invariance on the lattice.

## Abstract

We present a lattice gauge-fixing action $S_{gf}$ with the following properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_\mu \partial_\mu A_\mu)^2$, plus irrelevant terms of dimension six and higher; (b) $S_{gf}$ has a unique absolute minimum at $U_{x,\mu}=I$. Noting that the gauge-fixed action is not BRST invariant on the lattice, we discuss some important aspects of the phase diagram.