About bosonic rheonomic symmetry and the generation of a spin-1 field in D = 5 supergravity

In this paper we explicitly construct the bosonic sector of supergravity in 5-dimensions using the geometrical approach proposed in a previous publication. Starting from a first-order lagrangian written on an appropriate contraction of the Sp(8) group manifold we find that, in the second-order formalism the particle content of the theory is given by the graviton and by a massless spin-one self-interacting particle. The theory is proved to be factorized and rheonomic symmetrical. The rheonomic symmetry actually guarantees the necessary U(1) gauge invariance of the massless spin-one particle. The lagrangian for the spin-one field is the analogue of the lagrangian of the A_μν? field in D = 11 supergravity.