SU(N) chiral gauge theories on the lattice

TL;DR

This paper develops a non-perturbative lattice construction for SU(N) chiral gauge theories using equivariant gauge fixing, avoiding fermion doubling and handling Gribov copies, thus enabling a consistent continuum limit.

Contribution

It introduces a novel lattice gauge fixing method for non-abelian chiral gauge theories that overcomes previous no-go theorems and fermion doubling issues.

Findings

Successfully implements equivariant gauge fixing for SU(N) on the lattice.

Maintains unitarity and chiral fermion content through modified BRST identities.

Restores gauge invariance in the continuum limit via counter terms.

Abstract

We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the abelian case. The new ingredient allowing us to deal with the non-abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-abelian group (which we will take to be SU(N)) down to its maximal abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining abelian gauge symmetry. This modifies the equivariant BRST identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory.