Detecting topological sectors in continuum Yang-Mills theory and the fate of BRST symmetry

TL;DR

This paper introduces a new continuum gauge fixing method for Yang-Mills theories that isolates topological sectors, revealing sector-dependent BRST symmetry properties and implications for the structure of quantum states.

Contribution

It proposes a novel family of gauge fixings inspired by lattice Laplacian center gauges, enabling sector separation and analysis of BRST symmetry in continuum Yang-Mills theory.

Findings

Gauge fixing separates the partition function into topological sectors.

BRST symmetry exists within sectors but cannot be globally extended.

Partial contributions may be gauge-parameter independent, affecting quantum state space.

Abstract

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path-integral displays a BRST symmetry, however, it cannot be globally extended due to sector dependent boundary conditions on the ghost fields. These are nice features as they would permit to discuss the independence of the partial contributions on gauge parameters,, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.