T(T)over-bar Deformation of stress-tensor correlators from random geometry

We study stress-tensor correlators in the TT-deformed conformal field theories in two dimensions. Using the random geometry approach to the TT deformation, we develop a geometrical method to compute stress-tensor correlators. More specifically, we derive the TT deformation to the Polyakov-Liouville conformal anomaly action and calculate three and four-point correlators to the first-order in the TT 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 TT-deformed operator product expansions of the stress tensor. A salient feature of the TT-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.

Automated summary

In this study, stress-tensor correlators in TT-deformed conformal field theories in two dimensions were investigated using a geometrical method. The results reveal a logarithmic correction in the TT-deformed stress-tensor correlators, which is absent in lower-order functions but appears in the four-point function.