Chern-Simons Theory on Seifert 3-Manifolds

TL;DR

This paper develops a method to compute Chern-Simons theory on circle-bundle 3-manifolds by reducing the problem to a simpler Abelian theory on the base orbifold, simplifying calculations of the partition function.

Contribution

It introduces an Abelianisation technique that bypasses complex moduli space integrations, enabling explicit evaluation of the partition function on Seifert 3-manifolds.

Findings

Partition function reduced to 2D Abelian theory

Simplified computation on Seifert manifolds

Avoids non-Abelian moduli space integration

Abstract

We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of non-Abelian flat connections, reduces the complete partition function of the non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold S which is easily evaluated.