Induced Chern-Simons and WZW action in Noncommutative Spacetime

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 $\mathrm{th}--->0$, 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 $\mathrm{th}--->0$ 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.

Comments: LaTex, 13 pages, no figures; v2: refs added, add results for U(N) majorana spinors v3: clarification on p.5 and 6 concerning discussions of WZW. version to appear in NPB