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

Xing Huang; Chen-Te Ma

doi:10.1016/j.physletb.2019.134936

paper

The Probe of Curvature in the Lorentzian AdS $_{2}$ /CFT $_{1}$ Correspondence

arXiv:1907.01422 · doi:10.1016/j.physletb.2019.134936

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.

16 pages, minor changes, reference added

The Probe of Curvature in the Lorentzian AdS2​/CFT1​ Correspondence

Abstract

The Probe of Curvature in the Lorentzian AdS $_{2}$ /CFT $_{1}$ Correspondence