The probe of curvature in the Lorentzian AdS2/CFT1 correspondence

Abstract

We establish the Lorentzian AdS2/CFT1 correspondence from a reconstruction of all bulk points through the kinematic-space approach. The OPE block is exactly a bulk local operator. We formulate the correspondence between the bulk propagator in the non-interacting scalar field theory and the conformal block in CFT1. When we consider the stress tensor, the variation probes the variation of AdS2 metric. The reparameterization provides the asymptotic boundary of the bulk spacetime as in the derivation of the Schwarzian theory from two-dimensional dilaton gravity theory. Finally, we find the AdS2 Riemann curvature tensor based on the above consistent check.