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

TL;DR

This paper investigates the flat-space limit of holographic pseudo entropy in (A)dS spacetimes, showing how to recover entanglement entropy in flat spacetime from extremal surfaces in (A)dS, and relating it to ultra-relativistic limits in dual CFTs.

Contribution

It demonstrates a well-defined flat-space limit of holographic pseudo entropy in (A)dS spacetimes and connects it to entanglement entropy in dual flat spacetime theories.

Findings

Flat-space limit of extremal surfaces is well-defined in (A)dS.

Entanglement entropy in flat spacetime can be obtained from (A)dS pseudo entropy.

In dS spacetime, the extremal surface is inside the cosmological horizon.

Abstract

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.