Quantization of Chern-Simons Coefficient

TL;DR

This paper explores how the quantization of magnetic charge in (2+1)-dimensional QED leads to the quantization of the Chern-Simons coefficient, linking topological mass and magnetic monopoles.

Contribution

It establishes a direct relation between Dirac quantization of magnetic charge and the quantization of the Chern-Simons coefficient in (2+1)-dimensional QED.

Findings

Chern-Simons coefficient must be quantized with magnetic monopoles present

The quantization condition parallels the non-Abelian case

Links topological mass to magnetic charge quantization

Abstract

The relation between the Dirac quantization condition of magnetic charge and the quantization of the Chern-Simons coefficient is obtained. It implies that in a (2+1)-dimensional QED with the Chern-Simons topological mass term and the existence of a magnetic monopole with magnetic charge $g$, the Chern-Simons coefficient must be also quantized, just as in the non-Abelian case.