On the Quantization of the Chern-Simons Fields Theory on Curved Space-Times: the Coulomb Gauge Approach

TL;DR

This paper investigates the quantization of Chern-Simons field theory on curved space-times using Coulomb gauge, focusing on explicit calculations of propagators and vertices in specific expanding universe models.

Contribution

It provides explicit perturbative calculations of the propagator and vertices for Chern-Simons theory in curved backgrounds with Coulomb gauge, addressing a gap in understanding on such geometries.

Findings

Explicit propagator and vertex expressions in curved space-times

Perturbative analysis in Robertson-Walker and conformally static backgrounds

Clarification of gauge fixing effects in curved geometries

Abstract

We consider here the Chern-Simons field theory with gauge group SU(N) in the presence of a gravitational background that describes a two-dimensional expanding ``universe". Two special cases are treated here in detail: the spatially flat {\it Robertson-Walker} space-time and the conformally static space-times having a general closed and orientable Riemann surface as spatial section. The propagator and the vertices are explicitely computed at the lowest order in perturbation theory imposing the Coulomb gauge fixing.