Deligne-Beilinson cohomology and abelian links invariants

TL;DR

This paper explores abelian Chern-Simons theory using Deligne-Beilinson cohomology, deriving properties of observables and explicitly computing link invariants in specific 3-manifolds.

Contribution

It introduces a non-perturbative path-integral approach to compute abelian Chern-Simons link invariants using Deligne-Beilinson cohomology in various 3-manifolds.

Findings

Explicit link invariants for $S^3$, $S^1 imes S^2$, and $S^1 imes ext{Surface}_g$

Properties of observables in abelian Chern-Simons theory

Application of Deligne-Beilinson cohomology in quantum field theory

Abstract

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and we derive the main properties of the observables in a generic closed orientable 3-manifold. We present an explicit path-integral non-perturbative computation of the Chern-Simons links invariants in the case of the torsion-free 3-manifolds $S^3$, $S^1 \times S^2$ and $S^1 \times \Sigma_g$.