Time-like Entanglement Entropy: a top-down approach

TL;DR

This paper develops a top-down holographic method to compute time-like entanglement entropy in higher-dimensional quantum field theories, providing new analytic tools and revealing phase transitions in confining backgrounds.

Contribution

It introduces a robust prescription for calculating tEE in higher-dimensional QFTs, resolving previous ambiguities and extending the application to confining holographic backgrounds.

Findings

Analytic approximations for tEE and time-like separations

A stability criterion for bulk embeddings

Identification of phase transitions in confining backgrounds

Abstract

We investigate the concept of time-like entanglement entropy (tEE) within the framework of holography. We introduce a robust top-down prescription for computing tEE in higher-dimensional QFTs, both conformal and confining, eliminating the ambiguities typically associated with analytic continuation from Euclidean to Lorentzian signatures. We present accurate analytic approximations for tEE and time-like separations in slab geometries. We establish a clear stability criterion for bulk embeddings and demonstrate that tEE serves as a powerful tool for computing CFT central charges, extending and strengthening previous results. Finally, we apply our framework to holographic confining backgrounds, revealing distinctive behaviours like phase transitions.