Matter coupled F(4) supergravity and the AdS₆/CFT₅ correspondence

F(4) supergravity, the gauge theory of the exceptional six-dimensional Anti-de Sitter superalgebra, is coupled to an arbitrary number of vector multiplets whose scalar components parametrize the quaternionic manifold SO(4,n)/SO(4) × SO(n). By gauging the compact subgroup SU(2)_d⊗, where SU(2)_d is the diagonal subgroup of SO(4) ≃ SU(2)_L⊗SU(2)_R (the R-symmetry group of six-dimensional Poincaré supergravity) and is a compact group such that dim = n, we compute the scalar potential which, besides the gauge coupling constants, also depends in non-trivial way on the parameter m associated to a massive 2-form B_μν of the gravitational multiplet. The potential admits an AdS background for g = 3m, as the pure F(4)-supergravity. We compute the scalar squared masses (which are all negative) and retrieve the results dictated by AdS₆/CFT₅ correspondence from the conformal dimensions of boundary operators. The boundary F(4) superconformal fields are realized in terms of a singleton superfield (hypermultiplet) in harmonic superspace with flag manifold SU(2)/U(1) = S². We analize the spectrum of short representations in terms of superconformal primaries and predict general features of the K-K specrum of massive type-IIA supergravity compactified on warped AdS₆⊗S⁴.