A note on Gribov copies in 3D Chern-Simons theory

TL;DR

This paper constructs all Gribov copies in the Coulomb gauge for 3D Chern-Simons theory using harmonic maps and integrable systems, discussing implications for gauge fixing and vacuum structure.

Contribution

It provides a complete construction of Gribov copies in 3D Chern-Simons theory, a novel application of harmonic maps and integrable systems.

Findings

All Gribov copies in the Coulomb gauge are explicitly constructed.

Discussion on the impact of Gribov copies on gauge fixing and vacuum structure.

Brief insights into the implications for 3D QCD and modular regions.

Abstract

Using powerful tools of harmonic maps and integrable systems, all the Gribov copies in the Coulomb gauge in 3D Chern-Simons theory are constructed. Some issues about the Gribov and the modular re- gions are shortly discussed. The Gribov copies of the vacuum in 3D QCD in the Coulomb gauge are described. An interesting implication of the presence of Gribov copies is briefy pointed out.