A note on the holographic time-like entanglement entropy in Lifshitz theory

TL;DR

This paper investigates holographic time-like entanglement entropy in Lifshitz spacetime, comparing different proposals and analyzing the effects of anisotropic scaling, revealing that TEE can have both real and imaginary components.

Contribution

The study analytically compares multiple holographic proposals for TEE in Lifshitz backgrounds and explores the impact of anisotropic scaling on the entropy.

Findings

Different proposals yield the same TEE result in Lifshitz spacetime.

TEE in Lifshitz systems can have both real and imaginary parts.

Anisotropic parameter influences the TEE's complex structure.

Abstract

We explore the holographic time-like entanglement entropy (TEE) in the boundary theory of three-dimensional Lifshitz spacetime. There have been various holographic proposals for TEE in recent years and we test those proposals in the Lifshitz background. We obtain the analytic result for TEE in each proposal, compare the results, and analyze how the anisotropic scaling affects the TEE. We find that different holographic proposals give the same result for TEE in the Lifshitz background. Our analysis further suggests that the TEE of the Lifshitz system contains real and imaginary parts, both of which depend on the anisotropic parameter.