Some comments on Laplacian gauge fixing

TL;DR

This paper introduces a perturbative formulation of Laplacian gauge fixing on the lattice, compares it with Landau gauge, and discusses its renormalizability and implementation details.

Contribution

It provides the first perturbative formulation of Laplacian gauge fixing and compares it with traditional gauges on different geometries.

Findings

Laplacian gauge fixing can be implemented via a finite algorithm on the lattice.

A detailed comparison with Landau gauge is presented for toroidal and spherical geometries.

Renormalizability of the Laplacian gauge fixing remains to be demonstrated.

Abstract

Laplacian gauge fixing was introduced to find a unique representative of the gauge orbit, which on the lattice could be implemented by a ``finite'' algorithm. What was still lacking was a perturbative formulation of this gauge, which will be presented here. However, renormalizability is still to be demonstrated. For torodial and spherical geometries a detailed comparison with the Landau (or Coulomb) gauge will be made.