Gauged Six-Dimensional Supergravity from Warped IIB Reductions

TL;DR

This work constructs a complete non-linear Kaluza-Klein reduction from type IIB supergravity to Romans' six-dimensional $F(4)$ gauged supergravity on $S^2\times\Sigma$, with the reduction data encoded by a pair of holomorphic functions $\mathcal{A}_{\pm}$ on the Riemann surface $\Sigma$. The authors provide an explicit, fully nonlinear ansatz for the 10D fields that ensures the IIB equations of motion are equivalent to the 6D $F(4)$ equations of motion, thereby enabling any 6D solution to be uplifted to 10D. This framework generalizes prior reductions (notably Jeong:2013jfc) and encompasses the entire family of 1/2-BPS warped AdS$_6$ vacua found by DHoker et al., which are locally determined by $\mathcal{A}_{\pm}$. The construction offers a concrete bridge between 10D IIB AdS$_6$ backgrounds and 6D holographic dynamics, with potential extensions to include additional matter multiplets and explorations of non-BPS excitations in AdS$_6$/CFT$_5$ holography.

Abstract

We find a family of complete non-linear Kaluza-Kein reduction ansatze from type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic sector. The reduction is over a sphere $S^2$ and a Riemann surface $Σ$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $Σ$. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB supergravity that depend on these same functions $\mathcal{A}_{\pm}$.