Modified Lattice Landau Gauge

TL;DR

This paper introduces a modified lattice Landau gauge using stereographic projection to significantly reduce Gribov copies, potentially resolving the Gribov problem and the Neuberger 0/0 problem in lattice gauge theories.

Contribution

It presents a novel stereographic projection method for lattice Landau gauge that decreases Gribov copies exponentially and addresses longstanding gauge fixing issues.

Findings

Reduces Gribov copies exponentially in lattice gauge fixing.

Solves the Gribov problem for compact U(1) as a lattice artifact.

Potentially avoids the Neuberger 0/0 problem in SU(N) lattice formulations.

Abstract

We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.