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

In this work, we investigate the time evolution of the pseudo-(R\'enyi) 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-R\'enyi 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 $k^{\rm th}$ pseudo-R\'enyi entropy at the late time. Additionally, drawing inspiration from the gravitational side, specifically the gluing of two cutoff AdS geometries, we investigate the $k^{\rm th}$ pseudo-R\'enyi 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-R\'enyi entropy for globally deformed vacuum states.