Holographic Timelike Entanglement Entropy in Non-relativistic Theories

TL;DR

This paper explores how timelike entanglement entropy behaves in non-relativistic theories with broken Lorentz invariance, revealing its potential to encode stability, Fermi surfaces, and anisotropic features.

Contribution

It introduces the study of timelike entanglement entropy in non-relativistic theories with hyperscaling violation and Lifshitz anisotropy, highlighting its sensitivity to symmetry-breaking parameters.

Findings

Timelike entanglement entropy encodes stability and naturalness of theories.

It identifies Fermi surfaces via logarithmic or constant imaginary parts.

The imaginary part of the entropy offers a new interpretation of pseudoentropy.

Abstract

Timelike entanglement entropy is a complex measure of information that is holographically realized by an appropriate combination of spacelike and timelike extremal surfaces. This measure is highly sensitive to Lorentz invariance breaking. In this work, we study the timelike entanglement entropy in non-relativistic theories, focusing on theories with hyperscaling violation and Lifshitz-like spatial anisotropy. The properties of the extremal surfaces, as well as the timelike entanglement entropy itself, depend heavily on the symmetry-breaking parameters of the theory. Consequently, we show that timelike entanglement can encode, to a large extent, the stability and naturalness of the theory. Furthermore, we find that timelike entanglement entropy identifies Fermi surfaces either through the logarithmic behavior of its real part or, alternatively, via its constant imaginary part, with this constant value depending on the theory's Lifshitz exponent. This provides a novel interpretation for the imaginary component of this pseudoentropy. Additionally, we examine temporal entanglement entropy, an extension of timelike entanglement entropy to Euclidean space, and provide a comprehensive discussion of its properties in these theories.