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Black hole microstate counting and its macroscopic counterpart I

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In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.