Quantization Commutes with Reduction of Chern-Simons Gauge Theory

TL;DR

This paper proves that in the context of geometric quantization of Chern-Simons gauge theory on a genus one surface, the process of quantization commutes with the reduction procedure, using complex-analytic methods.

Contribution

It establishes an infinite-dimensional version of quantization commutes with reduction specifically for genus one Chern-Simons gauge theory, employing complex-analytic techniques.

Findings

Proved quantization commutes with reduction in genus one Chern-Simons theory.

Utilized complex-analytic methods involving the Atiyah-Bott stack.

Focused on the Chern-Simons line bundle in the proof.

Abstract

We prove an infinite-dimensional version of "quantization commutes with reduction" in the framework of geometric quantization of Chern-Simons gauge theory, focusing on the genus one case. The proof is complex-analytic and relies on the Atiyah-Bott stack and the Chern-Simons line bundle.