Supersymmetric AdS6 black holes from F(4) gauged supergravity

In F (4) gauged supergravity in six dimensions, we study supersymmetric AdS(6) black holes with various horizon geometries. We find a new AdS2x=0.25emsigma g1x sigma g2 horizon solution with g1>1 and g2>1, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically AdS(6) boundary and the AdS2x=0.25emsigma g1x sigma g2 horizon. We calculate the Bekenstein-Hawking entropy of the black hole and find a match with the recently calculated topologically twisted index of 5d USp(2N) gauge theory on sigma g1x sigma g2xS1 in the large N limit. We also find black hole horizons of Kahler four-cycles in Calabi-Yau fourfolds and on Cayley four-cycles in Spin(7) manifolds.