Further Study of BRST-Symmetry Breaking on the Lattice

TL;DR

This study investigates BRST-symmetry breaking in SU(2) gauge theory on the lattice by analyzing the Bose-ghost propagator across various lattice sizes, providing evidence of symmetry breaking related to the Gribov region.

Contribution

The paper provides a detailed lattice analysis of the Bose-ghost propagator, exploring discretization effects and continuum limits to understand BRST-symmetry breaking.

Findings

Q(p^2) prediction improves towards the continuum limit.

Nonzero Q(p^2) confirms BRST-symmetry breaking.

Results support the relation between Q(p^2) and gluon/ghost propagators.

Abstract

We evaluate the so-called Bose-ghost propagator Q(p^2) for SU(2) gauge theory in minimal Landau gauge, considering lattice volumes up to 120^4 and physical lattice extents up to 13.5 f. In particular, we investigate discretization effects, as well as the infinite-volume and continuum limits. We recall that a nonzero value for this quantity provides direct evidence of BRST-symmetry breaking, related to the restriction of the functional measure to the first Gribov region. Our results show that the prediction (from cluster decomposition) for Q(p^2) in terms of gluon and ghost propagators is better satisfied as the continuum limit is approached.