Semiclassical Approximation for Chern-Simons Theory and 3-Hyperbolic Invariants

TL;DR

This paper verifies the invariant integration method for Chern-Simons theory on hyperbolic 3-manifolds within the semiclassical approximation, providing insights into the partition function and related topological invariants.

Contribution

It introduces a semiclassical approach to Chern-Simons theory on hyperbolic 3-manifolds and discusses associated analytic torsion and eta invariants.

Findings

Verification of the invariant integration method in the semiclassical limit

Explicit expression for the partition function in the semiclassical approximation

Discussion of L^2 -analytic torsion and eta invariant for hyperbolic 3-manifolds

Abstract

The invariant integration method for Chern-Simons theory defined on the compact hyperbolic manifold {\Gamma}\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function is presented. We discuss briefly L^2 - analytic torsion and the eta invariant of Atiyah-Patodi-Singer for compact hyperbolic 3-manifolds.