Covariant gauge on the lattice: a new implementation

TL;DR

This paper introduces a novel lattice implementation of linear covariant gauges that overcomes previous limitations, enabling more accurate gauge fixing and preliminary analysis of gluon propagators in SU(2) gauge theory.

Contribution

A new lattice gauge fixing method based on a spin-glass model analogy that resolves issues from earlier approaches and allows for gauge parameter variation.

Findings

Successfully implements covariant gauges on the lattice.

Addresses and overcomes the no-go condition in previous methods.

Provides preliminary results for gluon propagators at different gauge parameters.

Abstract

We derive a new implementation of linear covariant gauges on the lattice, based on a minimizing functional that can be interpreted as the Hamiltonian of a spin-glass model in a random external magnetic field. We show that our method solves most problems encountered in earlier implementations, mostly related to the no-go condition formulated by L. Giusti, Nucl. Phys. B 498, 331 (1997). We carry out tests in the SU(2) case in four space-time dimensions. We also present preliminary results for the transverse gluon propagator at different values of the gauge parameter xi.