Abelian BF theory and Turaev-Viro invariant

TL;DR

This paper explores the U(1) BF quantum field theory using Deligne-Beilinson cohomology, revealing its connection to the U(1) Chern-Simons partition function and the abelian Turaev-Viro invariant, highlighting differences from non-abelian cases.

Contribution

It demonstrates the relationship between U(1) BF theory, U(1) Chern-Simons theory, and the abelian Turaev-Viro invariant using cohomological methods.

Findings

U(1) Chern-Simons partition function relates to U(1) BF theory.

U(1) BF theory coincides with abelian Turaev-Viro invariant.

Differences from non-abelian theories are clarified.

Abstract

The U(1) BF Quantum Field Theory is revisited in the light of Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant. Significant differences compared to the non-abelian case are highlighted.