Extremal Black Hole/CFT Correspondence in (Guaged) Supergravities

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 BekensteinHawking 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. Disciplines Physical Sciences and Mathematics | Physics 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 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/73 Extremal black hole/CFT correspondence in (gauged) supergravities David D.K. Chow, M. Cvetič, H. Lü, and C.N. Pope George and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6396, USA Division of Applied Mathematics and Theoretical Physics, China Institute for Advanced Study, Central University of Finance and Economics, Beijing, 100081, China DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 OWA, United Kingdom (Received 26 February 2009; published 10 April 2009) 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 nearhorizon 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 [ðD 1Þ=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 [ðD 1Þ=2] central charges each imply, via the Cardy formula, a microscopic entropy that agrees with the BekensteinHawking 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 1⁄4 4 and three charges in D 1⁄4 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. DOI: 10.1103/PhysRevD.79.084018 PACS numbers: 04.50.Gh, 04.60. m