Holographic torus correlators in $\text{AdS}_3$ gravity coupled to scalar field

Understand

This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS$_3$ gravity coupled with a free scalar field.

• Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein's equation and calculate mixed correlators for massless and massive coupled scalar fields.
• The conformal ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check.
• Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS$_3$/CFT$_2$ with non-trivial boundary topology.