3-dimensional low-energy topological invariants

TL;DR

This paper derives a one-loop approximation formula for a 3D abelian Donaldson-Witten theory, revealing it encodes topological invariants such as Reidemeister-Ray-Singer torsion and Betti numbers of the manifold.

Contribution

It introduces a one-loop approximation formula for 3D abelian Donaldson-Witten theory that captures key topological invariants of the manifold.

Findings

The formula includes Reidemeister-Ray-Singer torsion.

Betti numbers are explicitly contained in the expression.

The approach links quantum field theory to topological invariants.

Abstract

A description of the one-loop approximation formula for the partition function of a three-dimensional abelian version of the Donaldson-Witten theory is proposed. The one-loop expression is shown to contain such topological invariants of a three-dimensional manifold M like the Reidemeister-Ray-Singer torsion and Betti numbers.