Stochastic quantization of the Chern-Simons theory

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. Finally, we discuss the introduction of a non-trivial kernel as an alternative regularization.