Matter Coupled F(4) Gauged Supergravity Lagrangian

TL;DR

This paper constructs the complete Lagrangian for six-dimensional N=2 F(4) supergravity coupled to vector multiplets, enabling refined studies of the AdS_6/CFT_5 correspondence and supersymmetric structures.

Contribution

It provides the first explicit Lagrangian formulation of D=6, N=2 F(4) supergravity with vector multiplets, including gauged extensions and detailed superspace analysis.

Findings

Lagrangian for ungauged supergravity constructed

Extension to gauged supergravity with SU(2) x G symmetry achieved

Scalar potential and superspace structure elucidated

Abstract

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 AdS_6/CFT_5 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.