6D attractors and black hole microstates
Seyed Morteza Hosseini, Kiril Hristov, Achilleas Passias, Alberto Zaffaroni
TL;DR
This paper constructs new magnetically charged black hole horizons in a six-dimensional ${\rm F}(4)$ gauged supergravity truncation (arising from massive IIA on warped $AdS_6\times S^4$) and shows that their BPS entropy is captured by the topologically twisted index of the dual five-dimensional USp(2N) theory in the large $N$ limit. It establishes an explicit attractor mechanism in six-dimensional gauged supergravity by extremizing horizon area functionals $\mathcal{I}_{\text{AdS}_6}$, $\mathcal{I}_{\text{AdS}_4}$, and $\mathcal{I}_{\text{AdS}_2}$, which correspond to field theory quantities such as the $F_{S^5}$ free energy and the twisted index $\mathcal{I}_{\rm SCFT}$. The results provide a cohesive holographic picture across AdS$_6$, AdS$_4$, and AdS$_2$ horizons and demonstrate the correspondence $\mathcal{I}_{\rm SCFT}(\Delta_I)=\mathcal{I}_{\text{AdS}_2}(X^I)$ under $X^I=\Delta_I$, highlighting a generalized $\mathcal{I}$-extremization/attractor framework for matter-coupled ${\rm F}(4)$ theories.
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 Kähler-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.