Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2020)139
Keywords
AdS-CFT Correspondence; Conformal and W Symmetry; Conformal Field Theory
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Funding
- Ministry of Science and Technology (MOST) [107-2112-M-002-008]
- Program for Leading Graduate Schools, MEXT, Japan
- World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan
- JSPS [16H02182, 19K03863]
- Grants-in-Aid for Scientific Research [19K03863] Funding Source: KAKEN
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We consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into certain bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space-like separated. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones.
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