Abstract
In this article we probe the proposed holographic duality between $$ T\overline{T} $$
T
T
¯
deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$
T
T
¯
CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$
T
T
¯
CFT parameters.
Derivation of Equal-Time Commutators Involving the Symmetric Energy-Momentum Tensor and Applications