Holographic Timelike Entanglement Across Dimensions

TL;DR

This paper develops a holographic approach to compute timelike entanglement entropy in quantum field theories, extending existing methods to Lorentzian settings and analyzing various models to understand its scaling and phase behaviour.

Contribution

It introduces a holographic framework for timelike entanglement entropy applicable across dimensions and models, unifying conformal and nonconformal theories.

Findings

tEE scales universally with holographic central charge

Mass gaps modify tEE and affect phase behaviour

Robust scaling and phase distinctions between spacelike and timelike embeddings

Abstract

We develop a holographic framework for computing timelike entanglement entropy (tEE) in quantum field theories, extending the Ryu-Takayanagi prescription into Lorentzian settings. Using three broad classes of supergravity backgrounds, we derive both exact and approximate tEE expressions for slab, spherical, and hyperbolic regions, and relate them to the central charges of the dual conformal field theories. The method is applied to infinite families of supersymmetric linear quivers in dimensions from d=2 to d=6, showing that Liu-Mezei and slab central charges scale universally like the holographic central charge. We then analyse gapped and confining models, including twisted compactifications and wrapped brane constructions, identifying how a mass gap modifies tEE and when approximate formulas remain accurate. In all cases, we uncover robust scaling with invariant separations and signature dependent phase behaviour, distinguishing spacelike from timelike embeddings. Our results unify the treatment of tEE in both conformal and nonconformal theories, clarifying its role as a probe of causal structure, universal data, and nonperturbative dynamics in holography.