Gauged Six-Dimensional Supergravity from Warped IIB Reductions

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 $\Sigma$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $\Sigma$. 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 $\mathcal{A}_{\pm}$.