Toward an Effective CFT${}_2$ from $\mathcal{N}=4$ Super Yang-Mills and Aspects of Hawking Radiation

Abstract

Using $\mathcal{N}=4$ supersymmetric Yang-Mills theory we recover important aspects of the near-extremal thermodynamics of AdS${}_5$ black holes including both the outer and the inner horizons with their corresponding entropy and energy. This $\mathcal{N}=4$ supersymmetric Yang-Mills theory approach to black hole thermodynamics leads to an effective CFT${}_2$ interpretation similar to the work by Callan and Maldacena. We corroborate this effective CFT${}_2$ by implementing a particular near-horizon limit that geometrizes the Virasoro algebras as asymptotic symmetries. Using the effective CFT${}_2$ picture, we discuss aspects of the Hawking radiation rate for a region of the near-extremal AdS${}_5$ black hole quantum evolution.

arXiv comment26 pages, 1 figure; V2: Sec 4.2 expanded with details, and more references added; V3: A figure clarifying the supersymmetric and the extremal conditions is inserted. An alternative streamlined computation of the right central charge is now included. Results unchanged

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• $SL(3,\mathbb{Z})$ Modularity and New Cardy Limits of the $\mathcal{N}=4$ Superconformal Index
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• Retarded Green's Function from Rotating AdS Black Holes: Emergent CFT${}_2$ and Viscosity
• Explorations of Universality in the Entropy and Hawking Radiation of Non-Extremal Kerr AdS${}_4$ Black Holes