Year: 2025
Type: article
Abstract: A bstract In this work, we investigate the partition function of 2d CFT under root- $$ T\overline{T} $$ T T ¯ deformation. We demonstrate that the deformed partition function satisfies a flow equation. At large central charge sector, the deformed partition function reduces to a redefinition of the modular parameters, which preserves modular invariance under the deformed parameters. We then derive a Cardy-like formula for the asymptotic density of states using modular bootstrap trick. In the context of AdS/CFT, it was proposed the root- $$ T\overline{T} $$ T T ¯ deformed CFT corresponds to the AdS 3 with certain deformed boundary condition. We show the deformed BTZ black hole is a quotient of hyperbolic space. In terms of Chern-Simons formulation, we compute the root- $$ T\overline{T} $$ T T ¯ deformed BTZ black hole entropy and find that it obeys a Cardy-like formula, which is consistent with the modular bootstrap result. Furthermore, employing the Wilson spool technique, we compute the one-loop partition functions for the root- $$ T\overline{T} $$ T T ¯ deformed AdS 3 geometry. Our results reveal an exact agreement between one-loop gravitational partition function and the large c expansion of root- $$ T\overline{T} $$ T T ¯ deformed CFT partition function.
Source: Journal of High Energy Physics
Author: Miao He
Institution: Anhui Normal University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416759135