Pseudo entropy of primary operators in TT¯/JT¯-deformed CFTs

A bstract In this work, we investigate the time evolution of the pseudo-(Rényi) entropy after local primary operator quenches in 2D CFTs with 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 k 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 th pseudo-Rényi entropy for vacuum states characterized by distinct 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.