Extremal Static AdS Black Hole/CFT Correspondence in Gauged Supergravities

TL;DR

This work extends the extremal black hole/CFT correspondence to static charged AdS black holes in gauged supergravity by uplifting to higher dimensions where electric charges become internal angular momenta. Using a KK reduction framework, the near-horizon AdS$_2$ geometries uplift to warped S$^m$ bundles that yield Virasoro algebras with central charges $c_i = rac{6 k_i S_{BH}}{\\pi}$ and Frolov–Thorne temperatures $T_i$, so Cardy entropy reproduces the Bekenstein–Hawking entropy for D=4,5,6,7 examples. The results demonstrate a universal mechanism linking static extremal black holes to dual 2D CFTs via internal rotations, reinforcing the holographic interpretation of black hole microstates beyond rotating backgrounds. This provides a platform for exploring AdS$_2$/CFT$_1$ aspects of holography in gauged supergravities and string/M-theory uplifts.

Abstract

A recently proposed holographic duality allows the Bekenstein-Hawking entropy of extremal rotating black holes to be calculated microscopically, by applying the Cardy formula to the two-dimensional chiral CFTs associated with certain reparameterisations of azimuthal angular coordinates in the solutions. The central charges are proportional to the angular momenta of the black hole, and so the method degenerates in the case of static (non-rotating) black holes. We show that the method can be extended to encompass such charged static extremal AdS black holes by using consistent Kaluza-Klein sphere reduction ansatze to lift them to exact solutions in the low-energy limits of string theory or M-theory, where the electric charges become reinterpreted as angular momenta associated with internal rotations in the reduction sphere. We illustrate the procedure for the examples of extremal charged static AdS black holes in four, five, six and seven dimensions.