Localization & exact holography

A bstract We consider the AdS 2 /CFT 1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT 1 is given by the known quantum degeneracies of these black...

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Bibliographic Details
Published in:The journal of high energy physics 2013-04, Vol.2013 (4), p.1-32, Article 62
Main Authors: Dabholkar, Atish, Gomes, João, Murthy, Sameer
Format: Article
Language:English
Subjects:
Boundaries
Classical and Quantum Gravitation
Elementary Particles
Entropy
High energy physics
Holography
Integrals
Localization
Mathematical analysis
Mathematical models
Partitions
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
String Theory
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Summary:A bstract We consider the AdS 2 /CFT 1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT 1 is given by the known quantum degeneracies of these black holes. The bulk partition function is given by a functional integral over string fields in AdS 2 . Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons. Under reasonable assumptions about the relevant terms in the effective action, these integrals can be evaluated exactly to obtain a bulk partition function. It precisely reproduces all terms in the exact Rademacher expansion of the boundary partition function as nontrivial functions of charges except for the Kloosterman sum which can in principle follow from an analysis of phases in the background of orbifolded instantons. Our results can be regarded as a step towards proving ‘exact holography’ in that the bulk and boundary partition functions computed independently agree for finite charges. Since the bulk partition function defines the quantum entropy of the black hole, our results enable the evaluation of perturbative as well as nonperturbative quantum corrections to the Bekenstein-Hawking-Wald entropy of these black holes.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP04(2013)062