Hawking from Catalan

• Published in: The journal of high energy physics Vol. 2016; no. 5; pp. 1 - 26
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., Wang, Junpu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 12.05.2016; Springer Berlin
• Subjects: 1/N expansion; AdS-CFT correspondence; ASTRONOMY AND ASTROPHYSICS; black holes; Blocking; Charge; Classical and Quantum Gravitation; conformal and W symmetry; Elementary Particles; Exchange; Extrapolation; Gravitons; Operators (mathematics); Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Recursion; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Trees; AdS-CFT Correspondence; Conformal and W Symmetry; Black Holes; 1/N Expansion
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2016)069

A bstract The Virasoro algebra determines all ‘graviton’ matrix elements in AdS 3 /CFT 2 . We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT 2 operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in h H /c , the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation to sum the on-shell diagrams to all orders, computing the Virasoro vacuum block. Extrapolating to large h H /c determines the Hawking temperature of a BTZ black hole in dual AdS 3 theories.