A Cardy formula for off-diagonal three-point coefficients; or, how the geometry behind the horizon gets disentangled
arXiv:1804.08899 · doi:10.1007/JHEP09(2018)005
Abstract
In the AdS/CFT correspondence eternal black holes can be viewed as a specific entanglement between two copies of the CFT: the thermofield double. The statistical CFT Wightman function can be computed from a geodesic between the two boundaries of the Kruskal extended black hole and therefore probes the geometry behind the horizon. We construct a kernel for the AdS3/CFT2 Wightman function that is independent of the entanglement. This kernel equals the average off-diagonal matrix element squared of a primary operator. This allows us to compute the Wightman function for an arbitrary entanglement between the double copies and probe the emergent geometry between a left- and right-CFT that are not thermally entangled.
arXiv comment18 pages, 8 figures v2: Added appendix on spatial dependence, minor changes, matches published version
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