$T\bar{T}$ Deformation of Stress-Tensor Correlators from Random Geometry

Understand

We study stress-tensor correlators in the $T\bar{T}$-deformed conformal field theories in two dimensions.

• Using the random geometry approach to the $T\bar{T}$ deformation, we develop a geometrical method to compute stress-tensor correlators.
• More specifically, we derive the $T\bar{T}$ deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the $T\bar{T}$ 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 $T\bar{T}$-deformed operator product expansions of the stress tensor.