Deligne-Beilinson cohomology and abelian link invariants: torsion case

TL;DR

This paper computes abelian Chern-Simons link invariants in a torsion 3-manifold using Deligne-Beilinson cohomology, providing a non-perturbative path-integral approach for $SO(3)$.

Contribution

It introduces a non-perturbative path-integral method for computing link invariants in torsion 3-manifolds using Deligne-Beilinson cohomology.

Findings

Explicit path-integral computation of link invariants in $\, ext{R}P^3$

Demonstrates the use of Deligne-Beilinson cohomology in quantum field theory

Provides a framework for non-perturbative calculations in torsion cases

Abstract

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in $SO(3)\simeq\mathbb{R}P^3$, a toy example of 3-manifold with torsion.