TY - JOUR
T1 - Hawking from Catalan
AU - Fitzpatrick, A. Liam
AU - Kaplan, Jared
AU - Walters, Matthew T.
AU - Wang, Junpu
N1 - 19+8 pages, 5 figures
PY - 2016/5/12
Y1 - 2016/5/12
N2 - 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.
AB - 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.
KW - hep-th
U2 - 10.1007/JHEP05(2016)069
DO - 10.1007/JHEP05(2016)069
M3 - Article
SN - 1126-6708
VL - 2016
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
M1 - 69
ER -