A reciprocity formula from abelian BF and Turaev-Viro theories

Abstract

In this article we show that the use of Deligne-Beilinson cohomology in the context of the $U(1)$ BF theory on a closed 3-manifold $M$ yields a discrete ${\mathbb{Z}}_N$ BF theory whose partition function is an abelian TV invariant of $M$. By comparing the expectation values of the $U(1)$ and ${\mathbb{Z}}_N$ holonomies in both BF theories we obtain a reciprocity formula.

References in corpus (3)

• Turaev-Viro invariants as an extended TQFT
• Path-integral invariants in abelian Chern-Simons theory
• Abelian BF theory and Turaev-Viro invariant

Cited by in corpus (4)

• Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• 3D Topological Models and Heegaard Splitting I: Partition Function
• 3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables