Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2015)059
Keywords
Field Theories in Lower Dimensions; AdS-CFT Correspondence; Conformal and W Symmetry
Categories
Funding
- National Science Foundation [PHYS-1066293]
- National Science Foundation under CAREER Grant [PHY10-53842]
- European Research Council under the European Union's Seventh Framework Programme (FP7)
- ERC, Strongly Coupled Systems [STG 279943]
- Department of Energy [DE-FG02-91ER40671, DE-SC0009987]
- National Science and Engineering Research Council of Canada
- Direct For Mathematical & Physical Scien
- Division Of Physics [1053842] Funding Source: National Science Foundation
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We compute the contribution of the vacuum Virasoro representation to the genus-two partition function of an arbitrary CFT with central charge c > 1. This is the perturbative pure gravity partition function in three dimensions. We employ a sewing construction, in which the partition function is expressed as a sum of sphere four-point functions of Virasoro vacuum descendants. For this purpose, we develop techniques to efficiently compute correlation functions of holomorphic operators, which by crossing symmetry are determined exactly by a finite number of OPE coefficients; this is an analytic implementation of the conformal bootstrap. Expanding the results in 1/c, corresponding to the semiclassical bulk gravity expansion, we find that - unlike at genus one - the result does not truncate at finite loop order. Our results also allow us to extend earlier work on multiple-interval Renyi entropies and on the partition function in the separating degeneration limit.
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