Matter Coupled F(4) Gauged Supergravity Lagrangian

TL;DR

This work constructs the full matter-coupled $D=6$, $N=2$ $F(4)$ gauged supergravity by coupling vector multiplets with scalars on the coset $SO(4,n)/SO(4)\times SO(n)$ and deriving the Lagrangian via a geometric, rheonomic approach. Beginning with the ungauged theory and solving superspace Bianchi identities, it then implements a compact gauging of $SU(2)\times G$ and a mass parameter gauging with $\widehat{F}=F-mB$, revealing an $AdS_6$ supersymmetric background when $g=3m$ and a Higgs mechanism where the 2-form $B$ absorbs the singlet vector $A^0$. The complete gauged Lagrangian includes fermionic shifts, a scalar potential $\mathcal{W}$, and mass matrices, yielding an $AdS_6/CFT_5$-consistent spectrum that aligns with known representations and offers a robust framework for holographic studies and future KK analyses. The results provide a concrete, Lagrangian-level realization of the matter-coupled $F(4)$ theory and its AdS$_6$ vacua, enabling refined investigations of the dual 5D SCFTs and their flavor symmetries.

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.