Induced Chern-Simons and WZW action in Noncommutative Spacetime

TL;DR

This paper investigates the induced Chern-Simons and WZW actions in noncommutative gauge theories with fermions, revealing smooth and discontinuous limits depending on fermion type and highlighting UV/IR singularities.

Contribution

It computes the one-loop induced noncommutative Chern-Simons action for Dirac and Majorana fermions, revealing novel discontinuities and properties of the noncommutative WZW action.

Findings

Dirac fermion induces a smooth Chern-Simons limit as θ→0

Majorana fermion induces a finite jump in Chern-Simons term at θ→0

Discontinuity relates to UV/IR singularity phenomena

Abstract

We consider noncommutative gauge theory with Dirac or Majorana fermions in odd dimensional spacetime and compute the induced noncommutative Chern-Simons action generated at 1-loop. We observe that the Chern-Simons term induced by a Dirac fermion has a smooth limit when $\th ---> 0$, but there is a finite jump for the Chern-Simons term induced by a Majorana spinor. The induced Chern-Simons action from a Majorana spinor is nonvanishing even in the $\th ---> 0$ limit, a discontinuity that shares a similar characteristic as the UV/IR singularity discovered originally by Minwalla, Raamsdonk and Seiberg. Properties of the noncommutative WZW action are also discussed.