Correlation functions in TT*-deformed conformal field theories

I will begin by reviewing the TT* deformation of two dimensional field theories, and its formulation in terms of Jackiw-Teitelboim gravity. Then I will discuss how to compute correlation functions of local operators using this formulation, in which the position of the operators is defined using the dynamical coordinates of the formalism. I will focus on the large-momentum behavior of the two-point function when the undeformed theory is a conformal field theory. The main result (based on 2304.14091) is that for momentum q it is given by |q|^{-q^2/\pi |\Lambda|}, where 1/|\Lambda| is the deformation parameter. Interestingly, the sign of the exponent is different than previous computations which resummed the small momentum expansion. The decay at large momentum manifests the non-locality of the theory, which also appears through the fact that operators with different momentum require a different multiplicative renormalization, and that the large-momentum behavior of the correlation function on the torus is different from the behavior mentioned above on the plane.