Supersymmetric \(AdS_6\) black holes from ISO(3)\(\times \)U(1) F(4) gauged supergravity

Abstract

We study supersymmetric \(AdS_6\) 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 \(AdS_6\) vacuum with \(SO(3)\subset ISO(3)\) symmetry. We find a number of new supersymmetric \(AdS_2\times \mathcal {M}_4\) solutions by performing topological twists along \(\mathcal {M}_4\). For \(\mathcal {M}_4\) being a product of two Riemann surfaces \(\Sigma \times \widetilde{\Sigma }\), we perform a twist by \(SO(2)\times U(1)\) gauge fields and find \(AdS_2\times \Sigma \times \widetilde{\Sigma }\) 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 \(AdS_2\times \mathcal {M}_{\text {K}4}^-\) 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 \(AdS_2\times \mathcal {M}_{\text {C}4}^-\) solutions for negatively curved \(\mathcal {M}_{\text {C}4}\). We give numerical black hole solutions interpolating between all of these \(AdS_2\times \mathcal {M}_4\) near horizon geometries and the asymptotically locally \(AdS_6\) vacuum. It is also possible to uplift all of these solutions to type IIB theory via consistent truncations on \(S^2\times \Sigma \) leading to a new class of supersymmetric \(AdS_2\times \mathcal {M}_4\times S^2\times \Sigma \) solutions.