Duality Symmetry and the Cardy Limit

TL;DR

This paper investigates the duality symmetries and the Cardy limit of extremal black holes in Type IIA string theory, revealing conditions under which charges can be transformed to the Cardy limit, with implications for understanding black hole entropy.

Contribution

It demonstrates that generic charges cannot be generally transformed to the Cardy limit via dualities, but small charge modifications enable this in non-supersymmetric cases, advancing microscopic entropy calculations.

Findings

Generic charges cannot be brought to the Cardy limit by dualities.

Small fractional charge changes enable the Cardy limit in non-supersymmetric cases.

Results suggest potential for microscopic entropy determination of non-supersymmetric black holes.

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.