Quantization of the Chern-Simons coupling constant

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 F boolean AND F boolean AND A. 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 possibility.