Chern-Simons Theory as the Large Mass Limit of Topologically Massive Yang-Mills Theory

TL;DR

This paper demonstrates that quantum Chern-Simons theory can be derived as the large mass limit of topologically massive Yang-Mills theory, establishing a regularization approach and analyzing radiative corrections.

Contribution

It introduces a novel perspective linking Chern-Simons theory to the large mass limit of topologically massive Yang-Mills theory and proves UV finiteness of the latter.

Findings

No two-loop correction to the one-loop shift in the Chern-Simons level.

Topologically massive Yang-Mills theory is UV finite.

Radiative corrections up to second order are computed explicitly.

Abstract

We study quantum Chern-Simons theory as the large mass limit of the limit $D\to 3$ of dimensionally regularized topologically massive Yang-Mills theory. This approach can also be interpreted as a BRS-invariant hybrid regularization of Chern-Simons theory, consisting of a higher-covariant derivative Yang-Mills term plus dimensional regularization. Working in the Landau gauge, we compute radiative corrections up to second order in perturbation theory and show that there is no two-loop correction to the one-loop shift $k\rightarrow k+ c_{\scriptscriptstyle V},\,\,k$ being the bare Chern-Simons parameter. In passing we also prove by explicit computation that topologically massive Yang-Mills theory is UV finite.