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 ? T2, with duality group O(6,?22,?) ? SL(2,?). In the Cardy limit an internal circle combines with the AdS2 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.