Induced Chern–Simons and WZW action in noncommutative spacetime Original Research Article

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 θ→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 θ→0 limit, a discontinuity that share a similar characteristic as the UV/IR singularity discovered originally by Minwalla et al. Properties of the noncommutative WZW action are also discussed.