Correlation functions in TT -deformed theories on the torus

A bstract We study the correlation functions of local operators in unitary TT T T ¯ -deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation functions in momentum space when the undeformed theory is a conformal field theory. The large momentum behavior of the correlation functions is computed and compared to that of TT T T ¯ -deformed field theories defined on a plane. For the latter, the behavior found was ({t|q| e) }^-tq²{ } t q πe − tq 2 π, where q is the momentum and t is the deformation parameter. For a torus, the same behavior is found for | q | ≪ L / t, where L is the torus’ length scale. However, for | q | ≫ L / t, a different behavior is found: (2{{t⁵q²} e{L³|T|²}) }^tq²{ } 2 t 5 q 2 πe L 3 T 2 tq 2 π, where T is the complex structure of the torus. Hence, at large momentum, the correlator decays and then grows. This behavior suggests that operators carrying momentum q are smeared on a distance scale t | q |. The difference from the plane’s result illustrates the non-locality of the theory and the UV-IR mixing.