At the horizon of a supersymmetric AdS_5 black hole: Isometries and half-BPS giants

TL;DR

This work analyzes the near-horizon geometry of a supersymmetric AdS$_5$ black hole (Gutowski–Reall) by lifting to type IIB supergravity and solving the Killing spinor equations in both Poincaré and global AdS$_2$ patches. It shows the near-horizon solution preserves four supersymmetries and has the isometry supergroup $SU(1,1|1)\times SU(2)\times U(3)$, with the bosonic sector decomposing into $SL(2,\mathbb{R})\oplus U(1)$ and $SU(2)\oplus U(3)$ factors. The paper then identifies half-BPS D3-brane probes—giant and dual-giant-type—in both coordinate systems, deriving their equations of motion, kappa-symmetry conditions, and BPS energy relations; global-probe solutions require the AdS$_2$ origin ($\rho=0$) and yield explicit charge relations. These results illuminate the spectrum of BPS states in the near-horizon geometry and lay groundwork for microstate counting via quantization of these probes, with potential holographic ties to a dual quantum mechanics on the boundary.

Abstract

The near-horizon geometry of an asymptotically AdS_5 supersymmetric black hole discovered by Gutowski and Reall is analysed. After lifting the solution to 10 dimensions, we explicitly solve the Killing spinor equations in both Poincare and global coordinates. It is found that exactly four supersymmetries are preserved which is twice the number for the full black hole. The full set of isometries is constructed and the isometry supergroup is shown to be SU(1,1|1) X SU(2) X U(3). We further study half-BPS configurations of D3-branes in the near-horizon geometry in Poincare and global coordinates. Both giant graviton probes and dual giant graviton probes are found.