Study of Gribov Copies in the Yang-Mills ensemble

TL;DR

This paper investigates a new continuum quantization approach for Yang-Mills theory, focusing on the role of Gribov copies and the structure of gauge sectors labeled by center vortices, highlighting configurations free from Gribov ambiguities.

Contribution

It provides detailed analysis of the gauge fixing procedure in the new approach, demonstrating conditions under which configurations are free from Gribov copies and exploring the structure of vortex sectors.

Findings

Configurations in vortex-free sectors are free from Gribov copies.

Injectivity of the gauge mapping holds for typical configurations.

Simple vortex configurations also lack Gribov ambiguities.

Abstract

Recently, based on a new procedure to quantize the theory in the continuum, it was argued that Singer's theorem points towards the existence of a Yang-Mills ensemble. In the new approach, the gauge fields are mapped into an auxiliary field space used to separately fix the gauge on different sectors labeled by center vortices. In this work, we study this procedure in more detail. We provide examples of configurations belonging to sectors labeled by center vortices and discuss the existence of nonabelian degrees of freedom. Then, we discuss the importance of the mapping injectivity, and show that this property holds infinitesimally for typical configurations of the vortex-free sector and for the simplest example in the one-vortex sector. Finally, we show that these configurations are free from Gribov copies.