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arXiv · 1912.04105

The gravity dual of Lorentzian OPE blocks

Heng-Yu Chen·Lung-Chuan Chen·Nozomu Kobayashi·Tatsuma Nishioka
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Abstract

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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Heng-Yu Chen, Lung-Chuan Chen, Nozomu Kobayashi, Tatsuma Nishioka. 2019-12-09. The gravity dual of Lorentzian OPE blocks. https://doi.org/10.1007/jhep04(2020)139

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