Note on holographic torus stress tensor correlators in AdS3 gravity

A bstract In the AdS 3 /CFT 2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/ $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.