Hawking from Catalan

A. Liam Fitzpatrick, Jared Kaplan, Matthew T. Walters, Junpu Wang

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)
3 Downloads (Pure)


The Virasoro algebra determines all ‘graviton’ matrix elements in AdS3/CFT2. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT2 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 AdS3 theories.
Original languageEnglish
Article number69
JournalJournal of High Energy Physics
Publication statusPublished - 12 May 2016


  • hep-th


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