Supersymmetric AdS${}_6$ black holes from ISO(3)xU(1) F(4) gauged supergravity

We study supersymmetric $Ad{S}_6$ black holes from matter-coupled $F(4)$ gauged supergravity coupled to four vector multiplets with $ISO(3)\times U(1)$ gauge group. This gauged supergravity admits a maximally supersymmetric $Ad{S}_6$ vacuum with $SO(3)\subset ISO(3)$ symmetry. We find a number of new supersymmetric $Ad{S}_2\times {\mathcal{M}}_4$ solutions by performing topological twists along ${\mathcal{M}}_4$. For ${\mathcal{M}}_4$ being a product of two Riemann surfaces $\mathrm{\Sigma }\times \tilde{\mathrm{\Sigma }}$, we perform a twist by $SO(2)\times U(1)$ gauge fields and find $Ad{S}_2\times \mathrm{\Sigma }\times \tilde{\mathrm{\Sigma }}$ solutions for at least one of the Riemann surface being negatively curved. For ${\mathcal{M}}_4$ being a Kahler four-cycle ${\mathcal{M}}_{\text{K}4}$, a twist by $SO(2)\times U(1)$ gauge fields leads to $Ad{S}_2\times {\mathcal{M}}_{\text{K}4}^{-}$ solutions for negatively curved ${\mathcal{M}}_{\text{K}4}$. Finally, performing a twist by turning on $SO(3)$ gauge fields in the case of ${\mathcal{M}}_4$ being a Cayley four-cycle ${\mathcal{M}}_{\text{C}4}$ also leads to $Ad{S}_2\times {\mathcal{M}}_{\text{C}4}^{-}$ solutions for negatively curved ${\mathcal{M}}_{\text{C}4}$. We give numerical black hole solutions interpolating between all of these $Ad{S}_2\times {\mathcal{M}}_4$ near horizon geometries and the asymptotically locally $Ad{S}_6$ vacuum. It is also possible to uplift all of these solutions to type IIB theory via consistent truncations on $S^2\times \mathrm{\Sigma }$ leading to a new class of supersymmetric $Ad{S}_2\times {\mathcal{M}}_4\times S^2\times \mathrm{\Sigma }$ solutions.