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Journal of High Energy Physics

, 2015:109 | Cite as

Quantum entropy and exact 4D/5D connection

  • João GomesEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the AdS 2 /CFT 1 holographic correspondence near the horizon of rotating five-dimensional black holes preserving four supersymmetries in \( \mathcal{N}=2 \) supergravity. The bulk partition function is given by a functional integral over string fields in AdS 2 and is related to the quantum entropy via the Sen’s proposal. Under certain assumptions we use the idea of equivariant localization to non-rigid backgrounds and show that the path integral of off-shell supergravity on the near horizon background, which is a circle fibration over AdS 2 × S 2, reduces to a finite dimensional integral over n V + 1 parameters C A , where n V is the number of vector multiplets of the theory while the C 0 mode corresponds to a normalizable fluctuation of the metric. The localization solutions, which rely only on off-shell supersymmetry, become after a field redefinition, the solutions found for localization of supergravity on AdS 2 × S 2. We compute the renormalized action on the localization locus and show that, in the absence of higher derivative corrections, it agrees with the four dimensional counterpart computed on AdS 2 × S 2. These results together with possible one-loop contributions can be used to establish an exact connection between five and four dimensional quantum entropies.

Keywords

Black Holes in String Theory Superstrings and Heterotic Strings AdS-CFT Correspondence Supergravity Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.DAMTP, Center for Mathematical SciencesUniversity of CambridgeCambridgeU.K.

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