Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope

TL;DR

This paper demonstrates that noncommutative Chern-Simons theory can be consistently renormalized with no loop corrections in various gauges using a specific regularization scheme that preserves symmetries.

Contribution

It establishes a perturbative framework for noncommutative Chern-Simons theory with no loop corrections, employing a novel regularization and gauge-preserving approach.

Findings

No loop corrections to the 1PI functional in the chosen gauges

Use of Leibbrandt-Mandelstam prescription for propagators

Green functions are products of free propagators

Abstract

We show that the renormalized U(N) noncommutative Chern-Simons theory can be defined in perturbation theory so that there are no loop corrections to the 1PI functional of the theory in an arbitrary homogeneous axial (time-like, light-like or space-like) gauge. We define the free propagators of the fields of the theory by using the Leibbrandt-Mandelstam prescription --which allows Wick rotation and is consistent with power-counting-- and regularize its Green functions with the help of a family of regulators which explicitly preserve the infinitesimal vector Grassmann symmetry of the theory. We also show that in perturbation theory the nonvanishing Green functions of the elementary fields of the theory are products of the free propagators.