The Functional Measure of Gauge Theories in the Presence of Gribov Horizons

TL;DR

This paper develops a formal functional measure for gauge theories that maintains gauge symmetry in the presence of Gribov horizons, using lattice regularization and patching strategies to address gauge fixing ambiguities.

Contribution

It introduces a novel gauge-fixed measure framework that preserves Slavnov-Taylor identities amidst Gribov horizon complexities in lattice gauge theories.

Findings

Constructs a gauge-fixed measure compatible with Gribov horizon constraints.

Analyzes the continuum limit behavior of the measure in finite volume.

Provides a formal foundation for gauge theories with Gribov ambiguities.

Abstract

We discuss the formal structure of a functional measure for Gauge Theories preserving the Slavnov-Taylor identity in the presence of Gribov horizons. Our construction defines a gauge-fixed measure in the framework of the lattice regularization by dividing the configuration space into patches with different gauge-fixing prescriptions. Taking into account the bounds described by Dell'Antonio and Zwanziger we discuss the behaviour of the measure in the continuum limit for finite space-time volume.