D=4, N=2 supergravity in the presence of vector-tensor multiplets and the role of higher p-forms in the framework of free differential algebras

We thoroughly analyze at the bosonic level, in the framework of Free Differential Algebras (FDA), the role of 2-form potentials setting in particular evidence the precise geometric formulation of the anti-Higgs mechanism giving mass to the tensors. We then construct the (super)-FDA encoding the coupling of vector-tensor multiplets in D = 4, N = 2 supergravity, by solving the Bianchi identities in superspace and thus retrieving the full theory up to 3-fermions terms in the supersymmetry transformation laws, leaving the explicit construction of the Lagrangian to future work. We further explore the extension of the bosonic FDA in the presence of higher p-form potentials, focussing our attention to the particular case p = 3, which would occur in the construction of D = 5, N = 2 supergravity where some of the scalars are properly dualized.