Abstract
We study the map between two descriptions of the \( T\overline{T} \) deformation of conformal field theory (CFT): one is the defining description as a deformation of CFT by the \( T\overline{T} \)-operator. The other is an alternative description as the undeformed CFT on the dynamical \( T\overline{T} \)-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 \( T\overline{T} \)-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 \( T\overline{T} \)-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 \( T\overline{T} \)-deformed CFT, we focus on the correlators of semi-heavy operators, i.e., the operators of large conformal dimension ∆ ≫ \( \sqrt{c} \), and show an intuitive and simple way to obtain the \( T\overline{T} \)-deformed correlators from those of the undeformed CFT on the \( T\overline{T} \)-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.
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Acknowledgments
SH would like to thank Robert de Mello Koch for discussions and Ivonne Zavala for suggesting him an important reference. He also would like to thank the Departments of Mathematics and Physics at Nagoya University for hospitality and the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme, Black holes: bridges between number theory and holographic quantum information, where work on this paper was partially undertaken. This work was supported in part by EPSRC grant no EP/R014604/1 and the work of SH was supported in part by the National Natural Science Foundation of China under Grant No.12147219. The work of MS was supported in part by MEXT KAKENHI Grant Numbers 21K03552 and 21H0518.
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Hirano, S., Shigemori, M. Conformal field theory on \( T\overline{T} \)-deformed space and correlators from dynamical coordinate transformations. J. High Energ. Phys. 2024, 190 (2024). https://doi.org/10.1007/JHEP07(2024)190
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DOI: https://doi.org/10.1007/JHEP07(2024)190