Supersymmetry, Localization and Quantum Entropy Function

Understand

AdS_2/CFT_1 correspondence leads to a prescription for computing the degeneracy of black hole states in terms of path integral over string fields living on the near horizon geometry of the black hole.

• In this paper we make use of the enhanced supersymmetries of the near horizon geometry and localization techniques to argue that the path integral receives contribution only from a special class of string field configurations which are invariant under a subgroup of the supersymmetry transformations.
• We identify saddle points which are invariant under this subgroup.
• We also use our analysis to show that the integration over infinite number of zero modes generated by the asymptotic symmetries of AdS_2 generate a finite contribution to the path integral.