On the infrared limit of the Chern-Simons-Proca theory

TL;DR

This paper explores the infrared behavior of a modified 2+1D abelian Chern-Simons theory with a Proca mass, revealing connections between different topological quantum models through supersymmetry.

Contribution

It introduces a supersymmetric framework to analyze the infrared limit of the Chern-Simons-Proca theory and clarifies the relation between two topological models via phase-space reduction.

Findings

Supersymmetry explains the phase-space reduction between models

Partition functions are analyzed using equivariant cohomology

Infrared limit characterized by two distinct topological models

Abstract

We investigate a modification of the 2+1 dimensional abelian Chern-Simons theory, obtained by adding a Proca mass term to the gauge field. We are particularly interested in the infrared limit, which can be described by two {\it a priori} different "topological" quantum mechanical models. We apply methods of equivariant cohomology and the ensuing supersymmetry to analyze the partition functions of these quantum mechanical models. In particular, we find that a previously discussed phase-space reductive limiting procedure which relates these two models can be seen as a direct consequence of our supersymmetry.