The semiclassical approximation for the Chern-Simons partition function

TL;DR

This paper derives a semiclassical approximation for the Chern-Simons partition function using invariant integration, automatically accounting for volume factors and confirming agreement with Witten's exact results in specific cases.

Contribution

It introduces a new invariant integration method that simplifies the semiclassical approximation of the Chern-Simons partition function, fixing previous ambiguities.

Findings

Agreement with Witten's exact partition functions for SU(2)

Valid for various 3-manifolds including S^3 and torus bundles

Automatically incorporates volume and scale factors

Abstract

The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations are automatically taken account of in this framework. Agreement with Witten's exact expressions for the partition function in the weak coupling (large k) limit is verified for gauge group SU(2) and spacetimes S^3, S^2 x S^1, S^1 x S^1 x S^1 and L(p,q).