New supersymmetric AdS${}_6$ black holes from matter-coupled F(4) gauged supergravity

We study supersymmetric $Ad{S}_6$ black holes from matter-coupled $N=(1,1)$ gauged supergravity coupled to three vector multiplets and $SO(3)\times SO(3)$ gauge group. This gauged supergravity admits two supersymmetric $Ad{S}_6$ vacua preserving all supersymmetries with $SO(3)\times SO(3)$ and $SO(3{)}_{\text{diag}}$ symmetries. By considering a truncation to $SO(2{)}_{\text{diag}}\subset SO(3{)}_{\text{diag}}$ invariant sector, we find a number of new supersymmetric $Ad{S}_2\times {\mathcal{M}}_4$ solutions by performing a topological twist along ${\mathcal{M}}_4$. For ${\mathcal{M}}_4$ being a product of two Riemann surfaces $\mathrm{\Sigma }\times \tilde{\mathrm{\Sigma }}$ and a Kahler four-cycle, the twist is implemented by $SO(2{)}_{\text{diag}}$ gauge field while, for ${\mathcal{M}}_4$ given by a Cayley four-cycle, the twist is performed by turning on $SO(3{)}_{\text{diag}}$ gauge fields. We give numerical black hole solutions interpolating between $Ad{S}_2\times {\mathcal{M}}_4$ near horizon geometries and asymptotically locally $Ad{S}_6$ vacua. Among these solutions, there are solutions interpolating between both of the supersymmetric $Ad{S}_6$ vacua and near horizon geometries. The solutions can also be interpreted as holographic RG flows from five-dimensional SCFTs to superconformal quantum mechanics.