Non-perturbative BRST invariance and what it might be good for

TL;DR

This paper develops a lattice Yang-Mills theory with exact BRST invariance, modifying ghost sectors and regularizing Gribov horizons, potentially revealing new strong-interaction phases beyond confinement.

Contribution

It constructs a gauge-fixed lattice Yang-Mills theory with exact BRST invariance, addressing Neuberger's theorem and Gribov horizon issues.

Findings

Introduces a local lattice Yang-Mills theory with exact BRST invariance.

Modifies ghost sector to circumvent Neuberger's theorem.

Discusses potential new strong-interaction phases.

Abstract

We construct a local, gauge-fixed, lattice Yang-Mills theory with an exact BRST invariance, and with the same perturbative expansion as the standard Yang-Mills theory. The ghost sector, and some of its BRST transformation rules, are modified to get around Neuberger's theorem. A special term is introduced in the action to regularize the Gribov horizons, and the limit where the regulator is removed is discussed. We conclude with a few comments on what might be the physical significance of this theory. We speculate that there may exist new strong-interaction phases apart from the anticipated confinement phase.