Quantization of the Chern-Simons Coupling Constant

Abstract

We investigate the quantum consistency of p-form Maxwell-Chern-Simons electrodynamics in 3p+2 spacetime dimensions (for p odd). These are the dimensions where the Chern--Simons term is cubic, i.e., of the form FFA. For the theory to be consistent at the quantum level in the presence of magnetic and electric sources, we find that the Chern--Simons coupling constant must be quantized. We compare our results with the bosonic sector of eleven dimensional supergravity and find that the Chern--Simons coupling constant in that case takes its corresponding minimal allowed value.