Stochastic Quantization of the Chern-Simons Theory

TL;DR

This paper explores stochastic quantization of 3D non-Abelian Chern-Simons theory, demonstrating a proper regularization method that yields correct propagators and connecting it to 4D Topological Yang-Mills theories.

Contribution

It introduces a regulator in the Langevin equation for Chern-Simons theory, ensuring a well-defined equilibrium and establishing a link to 4D topological theories.

Findings

Regulator yields correct propagator

Equivalence between 3D Chern-Simons and 4D Topological Yang-Mills

Construction of topological invariants

Abstract

We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the correct propagator. We also analyze the connection between $d$=3 Chern-Simons and $d$=4 Topological Yang-Mills theories showing the equivalence between the corresponding regularized partition functions. We study the construction of topological invariants and the introduction of a non-trivial kernel as an alternative regularization.