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

Abstract

In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with $T\bar{T}/J\bar{T}$-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 $k^{\mathrm{th}}$ 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 $k^{\mathrm{th}}$ pseudo-Rényi entropy for vacuum states characterized by distinct $T\bar{T}$-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.

36 pages, 3 figure, v2, modified section 5