Hawking from Catalan
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 onshell 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. Here, we use this recursion relation to sum the onshell 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.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[2]}
 Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States); Boston Univ., Boston, MA (United States)
 John Hopkins Univ., Baltimore, MD (United States)
 Boston Univ., Boston, MA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0276SF00515
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 5; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; 1/N expansion; AdSCFT correspondence; black holes; conformal and W symmetry
 OSTI Identifier:
 1253729
Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., and Wang, Junpu. Hawking from Catalan. United States: N. p.,
Web. doi:10.1007/JHEP05(2016)069.
Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., & Wang, Junpu. Hawking from Catalan. United States. doi:10.1007/JHEP05(2016)069.
Fitzpatrick, A. Liam, Kaplan, Jared, Walters, Matthew T., and Wang, Junpu. 2016.
"Hawking from Catalan". United States.
doi:10.1007/JHEP05(2016)069. https://www.osti.gov/servlets/purl/1253729.
@article{osti_1253729,
title = {Hawking from Catalan},
author = {Fitzpatrick, A. Liam and Kaplan, Jared and Walters, Matthew T. and Wang, Junpu},
abstractNote = {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 onshell tree diagrams, organized in a perturbative expansion in hH/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. Here, we use this recursion relation to sum the onshell diagrams to all orders, computing the Virasoro vacuum block. Extrapolating to large hH/c determines the Hawking temperature of a BTZ black hole in dual AdS3 theories.},
doi = {10.1007/JHEP05(2016)069},
journal = {Journal of High Energy Physics (Online)},
number = 5,
volume = 2016,
place = {United States},
year = {2016},
month = {5}
}