Non-perturbative BRST symmetry and the spectral structure of the ghost propagator

TL;DR

This paper investigates the non-perturbative realization of BRST symmetry in Yang-Mills theory, revealing a discrepancy between continuum and lattice formulations through spectral analysis of ghost and gluon propagators.

Contribution

It demonstrates that the expected spectral interconnection from BRST symmetry is violated in lattice QCD data, indicating different realizations of the theory.

Findings

Spectral interconnection from BRST symmetry is violated in lattice data.

Continuum and lattice formulations of Yang-Mills are distinct.

Analysis supports non-perturbative BRST symmetry constraints are not universally realized.

Abstract

In BRST-quantised Yang-Mills theory the existence of BRST symmetry imposes significant constraints on the analytic structure of the continuum theory. In particular, the presence of this symmetry in the non-perturbative regime implies that any on-shell state with vanishing norm must have an associated partner state with identical mass, but negative inner product. In this work we demonstrate that for quantum chromodynamics (QCD) this constraint gives rise to an interconnection between the ghost and gluon spectra, and in doing so provides a non-trivial test of whether BRST symmetry is realised non-perturbatively. By analysing infrared lattice data for the minimal Landau gauge ghost propagator in pure $\mathrm{SU}(3)$ Yang-Mills theory, and comparing this with previous results for the gluon propagator, we show that this interconnection is violated, and hence conclude that continuum and current lattice formulations of Yang-Mills theory in Landau gauge represent two distinct realisations of the theory.