A reciprocity formula from abelian BF and Turaev-Viro theories

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 ZN BF theory whose partition function is an abelian TV invariant of M. By comparing the expectation values of the U(1) and ZN holonomies in both BF theories we obtain a reciprocity formula.