$ T\overline{T} $ Deformation of stress-tensor correlators from random geometry

We study stress-tensor correlators in the $$ T\overline{T} $$T T ¯ -deformed conformal field theories in two dimensions. Using the random geometry approach to the $$ T\overline{T} $$T T ¯ deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the $$ T\overline{T} $$T T ¯ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $$ T\overline{T} $$T T ¯ deformation from the deformed Polyakov-Liouville action. The results are checked against the standard conformal perturbation theory computation and we further check consistency with the $$ T\overline{T} $$T T ¯ -deformed operator product expansions of the stress tensor. A salient feature of the $$ T\overline{T} $$T T ¯ -deformed stress-tensor correlators is a logarithmic correction that is absent in two and three-point functions but starts appearing in a four-point function.