Abstract
\( T\overline{T} \) deformed CFTs with positive deformation parameter have been proposed to be holographically dual to Einstein gravity in a glue-on AdS3 spacetime [1]. The latter is constructed from AdS3 by gluing a patch of an auxiliary \( {\textrm{AdS}}_3^{\ast } \) spacetime to its asymptotic boundary. In this work, we propose a glue-on version of the Ryu-Takayanagi formula, which is given by the signed area of an extremal surface. The extremal surface is anchored at the endpoints of an interval on a cutoff surface in the glue-on geometry. It consists of an RT surface lying in the AdS3 part of the spacetime and its extension to the \( {\textrm{AdS}}_3^{\ast } \) region. The signed area is the length of the RT surface minus the length of the segments in \( {\textrm{AdS}}_3^{\ast } \). We find that the Ryu-Takayanagi formula with the signed area reproduces the entanglement entropy of a half interval for \( T\overline{T} \)-deformed CFTs on the sphere. We then study the properties of extremal surfaces on various glue-on geometries, including Poincaré AdS3, global AdS3, and the BTZ black hole. When anchored on multiple intervals at the boundary, the signed area of the minimal surfaces undergoes phase transitions with novel properties. In all of these examples, we find that the glue-on extremal surfaces exhibit a minimum length related to the deformation parameter of \( T\overline{T} \)-deformed CFTs.
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Acknowledgments
We are grateful to Bin Chen, Bartek Czech, Kanato Goto, Xia Gu, Monica Guica, Kangning Liu, Reiko Liu, Dominik Neuenfeld, Cheng Peng, Xiao-Liang Qi, Andrew Rolph, Shan-Ming Ruan, Tadashi Takayanagi, Huajia Wang, Jie-Qiang Wu and Yuan Zhong for helpful discussions. The work of LA was supported in part by the Dutch Research Council (NWO) through the Scanning New Horizons programme (16SNH02). The work of PXH, WXL, and WS is supported by the national key research and development program of China No. 2020YFA0713000. LA thanks the Asia Pacific Center for Theoretical Physics (APCTP) for hospitality during the focus program “Integrability, Duality and Related Topics”, as well as the Korea Institute for Advanced Study (KIAS) for hospitality during the “East Asia Joint Workshop on Fields and Strings 2022”, where part of this work was done. WXL and WS thank the Yukawa Institute for Theoretical Physics (YITP) for hospitality during the “YIPQS long-term workshop on Quantum Information, Quantum Matter and Quantum Gravity” (YITP-T-23-01), where part of this work was completed.
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Apolo, L., Hao, PX., Lai, WX. et al. Extremal surfaces in glue-on AdS/\( T\overline{T} \) holography. J. High Energ. Phys. 2024, 54 (2024). https://doi.org/10.1007/JHEP01(2024)054
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DOI: https://doi.org/10.1007/JHEP01(2024)054