New Topological Aspects of $BF$ Theories

TL;DR

This paper explores $BF$ theories on non trivial line bundles, revealing their connection to higher order bundles and showing how their partition functions differ from standard cases due to topological complexities.

Contribution

It demonstrates that $BF$ theories on non trivial line bundles realize non trivial higher order bundles and modifies the partition function accordingly.

Findings

Partition function differs from the usual by a factor from non trivial line bundles.

$BF$ theories over non trivial line bundles realize higher order bundles.

Partition function relates to Ray Singer Torsion.

Abstract

$BF$ theories defined over non trivial line bundles are studied. It is shown that such theories describe a realization of a non trivial higher order bundle. The partition function differs from the usual one -in terms of the Ray Singer Torsion- by a factor that arises from the non triviality of the line bundles.