# The Probe of Curvature in the Lorentzian AdS$_2$/CFT$_1$ Correspondence

## TL;DR

This paper reconstructs the Lorentzian AdS$_2$/CFT$_1$ correspondence using a kinematic-space approach, linking bulk operators to boundary conformal blocks and exploring curvature and metric variations.

## Contribution

It provides a detailed reconstruction of the AdS$_2$/CFT$_1$ correspondence, connecting bulk local operators, propagators, and the boundary Schwarzian theory.

## Key findings

- Bulk points reconstructed via kinematic space.
- Exact correspondence between OPE blocks and bulk local operators.
- Derived AdS$_2$ Riemann curvature tensor.

## Abstract

We establish the Lorentzian AdS$_2$/CFT$_1$ 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 CFT$_1$. When we consider the stress tensor, the variation probes the variation of AdS$_2$ 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 AdS$_2$ Riemann curvature tensor based on the above consistent check.