Nonrenormalization Theorem for Gauge Coupling in 2+1D

TL;DR

This paper proves that the gauge coupling in 2+1D gauge theories with various matter fields does not run, establishing a nonrenormalization theorem applicable to both Chern-Simons and topologically massive actions.

Contribution

It establishes a nonrenormalization theorem for the gauge coupling in 2+1D gauge theories with spinor and scalar matter fields, regardless of the gauge action used.

Findings

The $eta$-function of the gauge coupling is zero in these theories.

The result applies to both Chern-Simons and topologically massive gauge actions.

The theorem holds for any renormalizable matter system in 2+1D.

Abstract

We prove that $\be$-function of the gauge coupling in $2+1D$ gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.