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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
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. While the two-point scalar correlator is
accurately computed on the thermal AdS$_3$ saddle, the higher-point correlators
associated with scalar and stress tensor operators are explored.
