Quantum black holes, localization and the topological string

Understand

We use localization to evaluate the functional integral of string field theory on AdS_2xS^2 background corresponding to the near horizon geometry of supersymmetric black holes in 4d compactifications with N=2 supersymmetry.

• In particular, for a theory containing n_v + 1 vector multiplets, we show that the functional integral localizes exactly onto an ordinary integral over a finite-dimensional submanifold in the field space labeling a continuous family of instanton solutions in which auxiliary fields in the vector multiplets are excited with nontrivial dependence on AdS_2 coordinates.
• These localizing solutions are universal in that they follow from the off-shell supersymmetry transformations and do not depend on the choice of the action.
• They are parametrized by n_v +1 real parameters C^I, ; I= 0,..., n_v that correspond to the values of the auxiliary fields at the center of AdS_2.