## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

4-10-2009

#### Abstract

We extend the investigation of the recently proposed Kerr/conformal field theory correspondence to large classes of rotating black hole solutions in gauged and ungauged supergravities. The correspondence, proposed originally for four-dimensional Kerr black holes, asserts that the quantum states in the near-horizon region of an extremal rotating black hole are holographically dual to a two-dimensional chiral theory whose Virasoro algebra arises as an asymptotic symmetry of the near-horizon geometry. In fact, in dimension *D* there are [(*D* - 1)/2] commuting Virasoro algebras. We consider a general canonical class of near-horizon geometries in arbitrary dimension *D*, and show that in any such metric the [(*D* - 1)/2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the Bekenstein- Hawking entropy of the associated extremal black hole. In the remainder of the paper we show for most of the known rotating black hole solutions of gauged supergravity, and for the ungauged supergravity solutions with four charges in *D* = 4 and three charges in *D* = 5, that their extremal near-horizon geometries indeed lie within the canonical form. This establishes that, in all these examples, the microscopic entropies of the dual conformal field theories agree with the Bekenstein-Hawking entropies of the extremal rotating black holes.

#### Recommended Citation

Chow, D. D., Cvetič, M., Lü, H., & Pope, C. N. (2009). Extremal Black Hole/CFT Correspondence in (Guaged) Supergravities. Retrieved from http://repository.upenn.edu/physics_papers/73

**Date Posted:** 06 January 2011

This document has been peer reviewed.

## Comments

Suggested Citation:

Chow, D.D.K., M. Cvetič, H. Lü, and C.N. Pope. (2009)> "Extremal black hole/CFT correspondence in (gauged) supergravities."

Physical Review D.79, 084018.© 2009 The American Physical Society

http://dx.doi.org/10.1103/PhysRevD.79.084018