Quantum entropy and exact 4D/5D connection

• Published in: The journal of high energy physics 2015-01, Vol.2015 (1), p.1, Article 109
• Main Author: Gomes, João
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP01(2015)109

A bstract We consider the AdS 2 /CFT 1 holographic correspondence near the horizon of rotating five-dimensional black holes preserving four supersymmetries in 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.