  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)\times SO(n). By gauging the compact subgroup SU(2)_d \otimes G,
where SU(2)_d is the diagonal subgroup of SO(4)= SU(2)_L\otimes SU(2)_R (the
R-symmetry group of six-dimensional Poincare' supergravity) and G is a compact
group such that dim G = n. The potential admits an AdS background for g=3m, as
the pure F(4)-supergravity. 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)=S^2. 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 AdS_6\otimes S^4.
