Topological sectors and gauge invariance in massive vector-tensor theories in D ≥ 4

A family of locally equivalent models is considered. They can be taken as a generalization to d + 1 dimensions of the Topological Massive and “Self-dual” models in 2+1 dimensions. The corresponding 3+1 models are analized in detail. It is shown that one model can be seen as a gauge fixed version of the other, and their space of classical solutions differs in a topological sector represented by the classical solutions of pure BF model. The topological sector can be gauged out on cohomologically trivial base manifolds but on general settings it may be responsible of the difference in the long distance behaviour of the models. The presence of this topological sector appears explicitly in the partition function of the theories. The generalization of this models to higher dimensions is shown to be straightfoward.