Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling

TL;DR

This paper demonstrates that noncommutative pure Chern-Simons theory in axial gauge is free, with no higher order corrections or renormalization of the Chern-Simons coefficient, even at finite temperature.

Contribution

It provides a systematic analysis showing the absence of IR/UV mixing and higher order corrections in noncommutative Chern-Simons theory, establishing its free nature.

Findings

No IR/UV mixing in the theory.

Chern-Simons coefficient remains unrenormalized.

Ghosts decouple in axial gauge.

Abstract

We analyze the structure of noncommutative pure Chern-Simons theory systematically in the axial gauge. We show that there is no IR/UV mixing in this theory in this gauge. In fact, we show, using the usual BRST identities as well as the identities following from vector supersymmetry, that this is a free theory. As a result, the tree level Chern-Simons coefficient is not renormalized. It also holds that the Chern-Simons coefficient is not modified at finite temperature. As a byproduct of our analysis, we prove that the ghosts completely decouple in the axial gauge in a noncommutative gauge theory.