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Journal of High Energy Physics

Pseudo entropy of primary operators in $$ T\overline{T}/J\overline{T} $$-deformed CFTs

Song He, Jie Yang, Yu-Xuan Zhang, Zi-Xuan Zhao

Published Sep 5, 2023• 20 citations
Publisher

Abstract

Abstract In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with $$ T\overline{T}/J\overline{T} $$ T T ¯ / J T ¯ -deformation. Using perturbation theory, we analyze the corrections to the second pseudo-Rényi entropy at the late time, which exhibit a universal form, while its early-time behavior is model-dependent. Moreover, we uncover nontrivial time-dependent effects arising from the first-order deformation of the kth pseudo-Rényi entropy at the late time. Additionally, drawing inspiration from the gravitational side, specifically the gluing of two cutoff AdS geometries, we investigate the kth pseudo-Rényi entropy for vacuum states characterized by distinct $$ T\overline{T} $$ T T ¯ -deformation parameters, as well as for primary states acting on different deformed vacuum states. Our findings reveal additional corrections compared to the results of pseudo-Rényi entropy for globally deformed vacuum states.

DOI
10.1007/jhep09(2023)025

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Pseudo entropy of primary operators in TTˉT\bar{T}TTˉ/JTˉJ\bar{T}JTˉ-deformed CFTs
In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with TTˉ/JTˉT\bar T/J\bar TTTˉ/JTˉ-deformation. Using perturbation theory, we analyze the corrections to the second pseudo-Rényi entropy at the late time, which exhibit a universal form, while its early-time behavior is model-dependent. Moreover, we uncover nontrivial time-dependent effects arising from the first-order deformation of the kthk^{\rm th}kth pseudo-Rényi entropy at the late time. Additionally, drawing inspiration from the gravitational side, specifically the gluing of two cutoff AdS geometries, we investigate the kthk^{\rm th}kth pseudo-Rényi entropy for vacuum states characterized by distinct TTˉT\bar{T}TTˉ-deformation parameters, as well as for primary states acting on different deformed vacuum states. Our findings reveal additional corrections compared to the results of pseudo-Rényi entropy for globally deformed vacuum states.
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Correlation functions, entanglement and chaos in the TT‾/JT‾ T\overline{T}/J\overline{T} TT/JT-deformed CFTs
Abstract In this paper, we regard the TT‾/JT‾ T\overline{T}/J\overline{T} TT/JT T T ¯ / J T ¯ -deformed CFTs as perturbation theories and calculate the first order correction of the correlation functions due to the TT‾/JT‾ T\overline{T}/J\overline{T} TT/JT T T ¯ / J T ¯ ­deformation. As applications, we study the Rényi entanglement entropy of excited state in the TT‾/JT‾ T\overline{T}/J\overline{T} TT/JT T T ¯ / J T ¯ -deformed two-dimensional CFTs. We find, up to the first order perturbation of the deformation, the Rényi entanglement entropy of locally excited states will acquire a non­trivial time dependence. The excess of the Rényi entanglement entropy of locally excited state is changed up to order O(c). Furthermore, the out of time ordered correlation function is investigated to confirm that the TT‾/JT‾ T\overline{T}/J\overline{T} TT/JT T T ¯ / J T ¯ -deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.
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