Lattice Landau gauge via Stereographic Projection

TL;DR

This paper introduces a modified lattice Landau gauge using stereographic projection, reducing Gribov copies and avoiding the Neuberger 0/0 problem, thereby enabling more accurate gauge-fixed lattice QCD simulations.

Contribution

It proposes a new gauge fixing method on the lattice that minimizes Gribov copies and incorporates all copies in a BRST-consistent way, improving lattice QCD analysis.

Findings

Exponential reduction of Gribov copies in compact U(1)

No cancellation of Gribov copies in the stereographic projection framework

Potential resolution of discrepancies between lattice and continuum QCD studies

Abstract

The complete cancellation of Gribov copies and the Neuberger 0/0 problem of lattice BRST can be avoided in modified lattice Landau gauge. In compact U(1), where the problem is a lattice artifact, there remain to be Gribov copies but their number is exponentially reduced. Moreover, there is no cancellation of copies there as the sign of the Faddeev-Popov determinant is positive. Applied to the maximal Abelian subgroup this avoids the perfect cancellation amongst the remaining Gribov copies for SU(N) also. In addition, based on a definition of gauge fields on the lattice as stereographically-projected link variables, it provides a framework for gauge fixed Monte-Carlo simulations. This will include all Gribov copies in the spirit of BRST. Their average is not zero, as demonstrated explicitly in simple models. This might resolve present discrepancies between gauge-fixed lattice and continuum studies of QCD Green's functions.