6D attractors and black hole microstates

Abstract

We find a family of AdS$_2\times \mathcal{M}_4$ supersymmetric solutions of the six-dimensional $\mathrm{F}(4)$ gauged supergravity coupled to one vector multiplet that arises as a low energy description of massive type IIA supergravity on (warped) AdS$_6\times S^4$. $\mathcal{M}_4$ is either a K\"ahler-Einstein manifold or a product of two Riemann surfaces with a constant curvature metric. These solutions correspond to the near-horizon region of a family of static magnetically charged black holes. In the case where $\mathcal{M}_4$ is a product of Riemann surfaces, we successfully compare their entropy to a microscopic counting based on the recently computed topologically twisted index of the five-dimensional $\mathcal{N}=1$ $\mathrm{USp}(2 N)$ theory with $N_f$ fundamental flavors and an antisymmetric matter field. Furthermore, our results suggest that the near-horizon regions exhibit an attractor mechanism for the scalars in the matter coupled $\mathrm{F}(4)$ gauged supergravity, and we give a proposal for it.