Conformal field theory on $T\bar{T}$-deformed space and correlators from dynamical coordinate transformations
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| Format: | Preprint |
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2024
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| _version_ | 1866929242074251264 |
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| author | Hirano, Shinji Shigemori, Masaki |
| author_facet | Hirano, Shinji Shigemori, Masaki |
| contents | We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the undeformed CFT on the dynamical $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$-deformed CFT, we focus on the correlators of semi-heavy operators, i.e., the operators of large conformal dimension $Δ\gg\sqrt{c}$, and show an intuitive and simple way to obtain the $T\bar{T}$-deformed correlators from those of the undeformed CFT on the $T\bar{T}$-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_08278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal field theory on $T\bar{T}$-deformed space and correlators from dynamical coordinate transformations Hirano, Shinji Shigemori, Masaki High Energy Physics - Theory We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the undeformed CFT on the dynamical $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$-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 $T\bar{T}$-deformed CFT, we focus on the correlators of semi-heavy operators, i.e., the operators of large conformal dimension $Δ\gg\sqrt{c}$, and show an intuitive and simple way to obtain the $T\bar{T}$-deformed correlators from those of the undeformed CFT on the $T\bar{T}$-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. |
| title | Conformal field theory on $T\bar{T}$-deformed space and correlators from dynamical coordinate transformations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.08278 |