Interpolating between spacelike and timelike entanglement via holography

Abstract

We study entanglement entropy for slablike regions in quantum field theories, using their holographic duals. We focus on the transition between spacelike and timelike 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 timelike generalizations. We derive explicit expressions for the entanglement entropy in both conformal and confining cases and discuss their behavior 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 timelike separations in the confining field theory case.