Quantum black holes, localization, and the topological string
By A. Dabholkar, João Gomes, S. Murthy. 2010
167 citations recorded by the source corpus.
We use localization to evaluate the functional integral of string field theory on AdS2 × S2 background corresponding to the near horizon geometry of supersymmetric black holes in 4d compactifications with $ \mathcal{N} = 2 $ supersymmetry. In particular, for a theory containing nv + 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 AdS2 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 nv + 1 real parameters {CI; I = 0,…, nv} that correspond to the values of the auxiliary fields at the center of AdS2. In the Type-IIA frame, 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 off-shell values of scalar fields at the center of AdS2. In addition, there are contributions from one-loop determinants, brane-instantons, and nonperturbative orbifolds 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.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e25d1a81cec75dff831c1d1b9eb8571dedf21472
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Citations in the corpus
- Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions (2011, methodology): “Using supersymmetric localization we can get finite result for this integral by canceling the infinities from the bosonic zero mode integration against the zeroes from the fermion zero mode integration [67, 68].”
- Instantons on the 5-sphere and M5-branes (2012, background): “Also, studies of black hole partition function from 4d N = 2 supergravity [8] have been made.”
- Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates (2011, methodology): “[55, 56] attempted an exact evaluation of ZAdS2 using localization methods.”