Induced Chern-Simons and WZW action in noncommutative spacetime

We consider noncommutative gauge theory with Dirac or Majorana fermions in odd-dimensional spacetime and compute the induced noncommutative Chern-Simo ns action generated at 1-loop. We observe that the Chern-Simons term induce d by a Dirac fermion has a smooth limit when theta --> 0, but there is a fi nite jump for the Chern-Simons ten induced by a Majorana spinor. The induce d Chern-Simons action from a Majorana spinor is nonvanishing even in the th eta --> Limit, a discontinuity that share a similar characteristic as the U V/IR singularity discovered originally by Minwalla et al. Properties of the noncommutative WZW action are also discussed. (C) 2000 Elsevier Science B. V. All rights reserved.