On Level Quantization for the Noncommutative Chern-Simons Theory

TL;DR

This paper demonstrates that the coefficient in the noncommutative Chern-Simons theory must be quantized, extending the quantization condition to noncommutative spaces and other dimensions.

Contribution

It establishes the quantization condition for the Chern-Simons coefficient in noncommutative geometries, a novel extension of classical results.

Findings

The Chern-Simons coefficient is quantized on the noncommutative plane.

Quantization conditions also apply in other dimensions.

The work generalizes classical quantization results to noncommutative settings.

Abstract

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.