Heng-Yu ChenLung-Chuan ChenNozomu KobayashiTatsuma NishiokaHENG-YU CHEN2021-07-282021-07-28202011266708https://www.scopus.com/inward/record.uri?eid=2-s2.0-85083640687&doi=10.1007%2fJHEP04%282020%29139&partnerID=40&md5=814c91c8c1e26ce3ee3c0825a86f1f9bhttps://scholars.lib.ntu.edu.tw/handle/123456789/573470We 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. ? 2020, The Author(s).journal article10.1007/JHEP04(2020)1392-s2.0-85083640687