Reflected entropy and timelike entanglement in TT¯ -deformed CFT2s

Abstract

We develop a covariant formalism to investigate the mixed state entanglement between time-dependent boosted subsystems in TT¯-deformed CFT2s through the reflected entropy. To this end we utilize a conformal perturbation theory to obtain the Rényi reflected entropy through the partition function on the replica manifold. The correction to the reflected entropy to the first order in the deformation parameter μ is then obtained in the replica limit for finite temperature and finite-sized systems. We further perform an analytic continuation of our results to obtain the reflected entropy for timelike subsystems in such TT¯-deformed CFT2s. We verify our field theoretic computations for both spacelike and timelike subsystems by obtaining the dual EWCS in the corresponding bulk cutoff AdS3 geometries and find perfect agreement between the two. Published by the American Physical Society 2024