Two-Loop Finiteness of Chern-Simons Field Theory in Background Field Method

TL;DR

This paper demonstrates that Chern-Simons field theory remains finite at the two-loop level using a hybrid regularization method, highlighting its significance in conformal field theory and link invariants.

Contribution

It provides a detailed two-loop calculation showing the finiteness of Chern-Simons theory with a novel regularization approach.

Findings

Chern-Simons theory is finite at two loops

Hybrid regularization effectively handles divergences

Supports connections to conformal field theory and link invariants

Abstract

We perform two-loop calculation of Chern-Simons in background field method using the hybrid regularization of higher-covariant derivative and dimensional regularization. It is explicitly shown that Chern-Simons field theory is finite at the two-loop level. This finiteness plays an important role in the relation of Chern-Simons theory with two-dimensional conformal field theory and the description of link invariant.