Abelian Chern-Simons theory as the strong large-mass limit of topologically massive abelian gauge theory: the Wilson loop

TL;DR

This paper demonstrates that the Wilson loop expectation value in topologically massive abelian gauge theory approaches that of abelian Chern-Simons theory as the mass becomes large, establishing a connection between the two theories.

Contribution

It shows the large-mass limit of topologically massive abelian gauge theory reproduces the Wilson loop of abelian Chern-Simons theory, clarifying their relationship.

Findings

Large-mass limit of the gauge theory matches Chern-Simons Wilson loop expectations.

Renormalized vacuum expectation values are well-defined in both theories.

The connection provides insights into topological aspects of gauge theories.

Abstract

We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in $\RR^3$ can be defined so that its large-mass limit be the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in $\RR^3$.