Duality Symmetry and the Cardy Limit

Abstract

We study supersymmetric and non-supersymmetric extremal black holes obtained in Type IIA string theory compactified on K3 X T^2, with duality group O(6,22,Z) X SL(2,Z). In the Cardy limit an internal circle combines with the AdS_2 component in the near horizon geometry to give a BTZ black hole whose entropy is given by the Cardy formula. We study black holes carrying D0-D4 and D0-D6 brane charges. We find, both in the supersymmetric and non-supersymmetric cases, that a generic set of charges cannot be brought to the Cardy limit using the duality symmetries. In the non-supersymmetric case, unlike the supersymmetric one, we find that when the charges are large, a small fractional change in them always allows the charges to be taken to the Cardy limit. These results could lead to a microscopic determination of the entropy for extremal non-supersymmetric black holes, including rotating cases like the extreme Kerr black hole in four dimensions.

46 pages, Latex, Some comments added in Introduction and Conclusions. Minor changes made in sections 3.4 and 5

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• Cardy and Kerr
• Superconformal Quantum Mechanics from M2-branes
• Indefinite theta functions and black hole partition functions
• Generating new $N=2$ small black holes
• New Perspectives on Attractor Flows and Trees from CFT
• Generalized Hot Attractors
• An SLE approach to four dimensional black hole microstate entropy
• The Hot Attractor Mechanism: Decoupling Without Deep Throats