Quantization of the Chern-Simons Coupling Constant

TL;DR

This paper studies the quantum consistency of p-form Maxwell-Chern-Simons theories in specific dimensions, showing that the Chern-Simons coupling must be quantized for consistency, with implications for supergravity.

Contribution

It demonstrates the quantization condition of the Chern-Simons coupling in certain dimensions and relates it to the minimal value in eleven-dimensional supergravity.

Findings

Chern-Simons coupling must be quantized for quantum consistency

The minimal coupling value matches that in eleven-dimensional supergravity

Provides a consistency check for higher-dimensional gauge theories

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.