Speaker
Description
Massive Abelian p-form gauge theories possess dualities that hold classically, but may be broken at the quantum level in non-trivial topological spacetimes. We demonstrate this in the BF model for massive gauge theories in d dimensions, where a p-form and a (d-p-1)-form are topologically coupled together in a gauge invariant way. Integrating out the (d-p-1)-form from its equation of motion results in a massive p-form and vice versa. We then show that in the path integral quantisation of the theory, integrating out the (d-p-1)-form results in a determinant that is different to that when integrating out the p-form. This difference is dependent on the topology of spacetime, resulting in different counterterms for renormalising their divergences. We compute these counterterms for a few non-trivial topological spacetimes, explicitly showing that the duality is broken at the quantum level.