Conformal field theory on TT̄-deformed space and correlators from dynamical coordinate transformations

This is the authors' abstract. We don't add key points for this paper.

We study the map between two descriptions of the TT̄ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the TT̄-operator. The other is an alternative description as the undeformed CFT on the dynamical TT̄-deformed space that backreacts to the state or operator insertions, reminiscent of the theory of gravity. Instead of adopting the topological gravity description, we develop a more literal CFT-based operator formalism that facilitates systematic and straightforward computations of the TT̄-deformation of the stress tensor, operators, and their correlators, while rederiving known results in the literature. Along the way, we discuss the backreaction to the TT̄-deformed space in response to local operators and exhibit the hard-disk and free-space structures in the UV-cutoff and Hagedorn phases, respectively, suggested by Cardy-Doyon and Jiang. To capitalize on the alternative description of the TT̄-deformed CFT, we focus on the correlators of semi-heavy operators, i.e., the operators of large conformal dimension Δ√c, and show an intuitive and simple way to obtain the TT̄-deformed correlators from those of the undeformed CFT on the TT̄-deformed space via dynamical coordinate transformations. This may have implications in the holographic dual description, pointing towards a working dictionary for a class of matter correlators in the cutoff AdS picture.