A one-loop exact quantization of Chern-Simons theory

TL;DR

This paper presents a novel gauge approach that enables a one-loop exact quantization of Chern-Simons theory, revealing insights into its structure and relation to boundary theories like chiral WZW models.

Contribution

It introduces a new gauge fixing method that allows for exact quantization at one-loop, advancing understanding of Chern-Simons and related 3D theories.

Findings

Achieves one-loop exact quantization of Chern-Simons theory.

Clarifies the bulk-boundary correspondence with chiral WZW theory.

Extends the approach to a class of related 3D theories.

Abstract

We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF theory and Chern-Simons theory. This approach illuminates several important features of Chern-Simons theory, notably the bulk-boundary correspondence of Chern-Simons theory with chiral WZW theory. In addition to rigorously constructing the theory, we also explain how it applies to a large class of closely related 3-dimensional theories and some of the consequences for factorization algebras of observables.