Supersymmetry, localization and quantum entropy function. (English) Zbl 1270.81150
Summary: \(\text{AdS}_2/\text{CFT}_1\) 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 \(\text{AdS}_2\) generate a finite contribution to the path integral.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83C57 | Black holes |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81S40 | Path integrals in quantum mechanics |
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