Cohomological localization of Chern-Simons theory

TL;DR

This paper extends the cohomological localization framework for Chern-Simons theory to all Seifert manifolds by topologically twisting the supersymmetric model, enabling exact path integral computations including Wilson loops.

Contribution

It generalizes the cohomological localization method to Seifert manifolds and incorporates Wilson loop calculations within this framework.

Findings

Localization applies to all Seifert manifolds.

Wilson loop expectation values are computed explicitly.

The approach connects with existing exact path integral methods.

Abstract

We generalize the framework introduced by Kapustin et al. for doing path integral localization in Chern-Simons theory to work on any Seifert manifold. This is done by topologically twisting the supersymmetric theory considered by Kapustin et al., after which the theory takes a cohomological form. We also consider Wilson loops which wrap the fiber directions and compute their expectation values. We discuss the relation with other approaches to exact path integral calculations in Chern-Simons theory.