Gauge-fixing on the Lattice via Orbifolding

TL;DR

This paper proposes a novel orbifolding approach to gauge-fixing on the lattice that addresses the Neuberger 0/0 problem, ensuring orbit independence and viability for lattice gauge theories.

Contribution

It introduces an orbifolding modification of lattice Landau gauge, circumventing the Neuberger problem and analyzing its mathematical properties using Morse theory and algebraic geometry.

Findings

Orbifolding modifies gauge-fixing to avoid the Neuberger 0/0 problem.

The new gauge-fixing approach ensures orbit independence in lattice gauge theories.

The partition function remains orbit independent except in a measure-zero region.

Abstract

When fixing a covariant gauge, most popularly the Landau gauge, on the lattice one encounters the Neuberger 0/0 problem which prevents one from formulating a Becchi--Rouet--Stora--Tyutin symmetry on the lattice. Following the interpretation of this problem in terms of Witten-type topological field theory and using the recently developed Morse theory for orbifolds, we propose a modification of the lattice Landau gauge via orbifolding of the gauge-fixing group manifold and show that this modification circumvents the orbit-dependence issue and hence can be a viable candidate for evading the Neuberger problem. Using algebraic geometry, we also show that though the previously proposed modification of the lattice Landau gauge via stereographic projection relies on delicate departure from the standard Morse theory due to the non-compactness of the underlying manifold, the corresponding gauge-fixing partition function turns out to be orbit independent for all the orbits except in a region of measure zero.