Localization and Exact Quantum Entropy of Black Holes

by Atish Dabholkar

Tuesday 18 Jan 2011, 14:00 → 15:00 Europe/Zurich

TH Theory Conference Room (CERN)

We use localization to evaluate the functional integral of string field theory on the AdS2 near horizon geometry of supersymmetric black holes in 4d compacti cations with N = 2 supersymmetry. We show that in a theory with nv +1 vector multiplets, the functional integral localizes exactly onto an ordinary integral over a ( nv + 1)-dimensional submanifold in the fi eld space labeling a continuous family of complex instanton solutions in which auxiliary elds in the vector multiplets are excited with nontrivial dependence on AdS2 coordinates. These localizing solutions are universal in that they follow from the o -shell supersymmetry transformations and do not depend on the choice of the action. Assuming D-terms evaluate to zero on the solutions for reasons of supersymmetry, the classical part of the integrand equals the absolute square of the partition function of the topological string as conjectured by Ooguri, Strominger, and Vafa; however evaluated at the o -shell values of scalar elds at the center of AdS2. In addition, there are contributions from one-loop determinants, brane-instantons, and nonperturbative orbiolds that are in principle computable. These results thus provide a concrete method to compute exact quantum entropy of these black holes including all perturbative and nonperturbative corrections and can be used to establish a precise relation between the quantum degeneracies of black holes and the topological string.