On the Role of Vector Supersymmetry in Topological Field Theory

TL;DR

This paper explores how vector supersymmetry influences the construction of gauge-invariant quantities and the cancellation of ultraviolet divergences in topological field theories, exemplified by three-dimensional Chern-Simons theory.

Contribution

It clarifies the role of vector supersymmetry in topological field theories and provides detailed analysis using Chern-Simons theory as a case study.

Findings

Vector supersymmetry aids in constructing gauge-invariant quantities.

It contributes to the cancellation of ultraviolet divergences.

Detailed analysis of Chern-Simons theory illustrates these roles.

Abstract

Vector supersymmetry is typical of topological field theory. Its role in the construction of gauge invariant quantities is explained, as well as its role in the cancellation of the ultraviolet divergences. The example of the Chern-Simons theory in three dimensions is treated in details.