Flat-Space Limit of Holographic Pseudo Entropy in (A)dS Spacetimes

The real part of pseudo entropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual dS and AdS spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultra-relativistic limit of pseudo entropy in the dual CFT to (A)dS spacetimes.