Matter Coupled F(4) Supergravity and the AdS_6/CFT_5 Correspondence

TL;DR

This work constructs matter-coupled F(4) gauged supergravity in six dimensions with vector multiplets whose scalars live on the coset SO(4,n)/SO(4)×SO(n). By gauging SU(2)_d⊗G and including a mass parameter m from a gravitational 2-form, the authors derive the scalar potential and show a supersymmetric AdS6 vacuum arises only for g=3m, with scalar masses matching AdS6/CFT5 expectations. They formulate the boundary theory in harmonic superspace via a singleton hypermultiplet, revealing two towers of short F(4) representations and predicting the KK spectrum of massive Type IIA on warped AdS6×S^4. The results establish a detailed bulk/boundary correspondence in six dimensions and constrain the structure of the dual 5d conformal field theory through symmetry and representation theory.

Abstract

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 $SU(2)_d \otimes \cG$, where SU(2)_d is the diagonal subgroup of $SO(4)\simeq SU(2)_L\otimes SU(2)_R$ (the R-symmetry group of six-dimensional Poincaré supergravity) and $\cG$ is a compact group such that $dim\cG = n$, 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 AdS_6/CFT_5 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)=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 $AdS_6\otimes S^4$.