Vector field mass generation in a single D = 4 topological BF model

Starting from some of our previous results on D = 4 consistent nontrivial cross-couplings between a topological BF model and a finite collection of massless real scalar fields under precise selection rules, here we extend this analysis to the case where the matter scalars are purely massive or at least partially massive and show that the possibility of endowing the U(1) BF vector field with a mass term requires at least one massless matter component. These results are encouraging at further expanding the D = 4 analysis to a more complex situation, where the single topological BF model is replaced by a finite set of such models. Given the known relationship between topological BF models and various gravity and super-gravity theories in D = 4, the latter approach will hopefully shed some light on viable mass scenarios in such gravitationally-coupled gauge systems.Starting from some of our previous results on D = 4 consistent nontrivial cross-couplings between a topological BF model and a finite collection of massless real scalar fields under precise selection rules, here we extend this analysis to the case where the matter scalars are purely massive or at least partially massive and show that the possibility of endowing the U(1) BF vector field with a mass term requires at least one massless matter component. These results are encouraging at further expanding the D = 4 analysis to a more complex situation, where the single topological BF model is replaced by a finite set of such models. Given the known relationship between topological BF models and various gravity and super-gravity theories in D = 4, the latter approach will hopefully shed some light on viable mass scenarios in such gravitationally-coupled gauge systems.