Interpolating between Space-like and Time-like Entanglement via Holography

TL;DR

This paper explores how entanglement entropy in quantum field theories transitions between space-like and time-like separations using holographic duals, identifying new classes of extremal surfaces and their analytic continuations.

Contribution

It introduces two classes of extremal surfaces, Type I and Type II, that interpolate between space-like and time-like entanglement, extending the Ryu Takayanagi prescription.

Findings

Explicit formulas for entanglement entropy in conformal and confining backgrounds.

Identification of phase transition behaviors in entanglement entropy.

Existence of Ryu Takayanagi surfaces for time-like separations in confining theories.

Abstract

We study entanglement entropy for slab like regions in quantum field theories, using their holographic duals. We focus on the transition between space like and time like separations. By considering boosted subsystems in conformal and confining holographic backgrounds, we identify two classes of extremal surfaces: real ones (Type I) and complex surfaces (Type II). These interpolate between the usual Ryu Takayanagi prescription and its time like generalisations. We derive explicit expressions for the entanglement entropy in both conformal and confining cases. We discuss their behaviour across phase transitions and null limits. The interpolation between Type I and Type II surfaces reveals an analytic continuation of the extremal surface across the light cone. Our analysis also finds the existence of a Ryu Takayanagi surface (Type I) even for time like separations in the confining field theory case.