Matter Coupled F(4) Gauged Supergravity Lagrangian

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We construct the so far unknown Lagrangian of D=6, N=2 F(4) Supergravity coupled to an arbitrary number of vector multiplets whose scalars span the coset manifold SO(4,n)/SO(4) x SO(n). This is done first in the ungauged case and then extended to the compact gauging of SU(2) x G, where SU(2) is the R-symmetry diagonal subgroup of SU(2)ₗ x SU(2)ᵣ = SO(4) and G is a compact subgroup of SO(n), n being the number of vector multiplets, and such that dim G = n. The knowledge of the Lagrangian allows in principle to refine the AdS₆/CFT₅ correspondence already discussed, as far as supersymmetric multiplets are concerned, in a previous related paper. With respect to the latter we also give a more exaustive treatment of the construction of the theory at the level of superspace Bianchi identities and in particular of the scalar potential.