Topological Sectors and Gauge invariance in massive Vector-Tensor Theories in D >=4

TL;DR

This paper explores a family of massive vector-tensor models in four or more dimensions, analyzing their gauge invariance, topological sectors, and implications for long-distance behavior, extending known 2+1 dimensional models.

Contribution

It generalizes topological massive and self-dual models to higher dimensions and clarifies their gauge relations and topological sectors.

Findings

Models are gauge equivalent up to a topological sector.

Topological sectors influence the models' long-distance behavior.

Partition functions explicitly reflect the topological contributions.

Abstract

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 a 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.