Holographic Timelike Entanglement Entropy from Rindler Method

TL;DR

This paper extends the concept of entanglement entropy to timelike regions using the Rindler method, providing a gravitational dual description and refining the cut-off concept for Lorentzian theories.

Contribution

It introduces a refined cut-off for timelike regions and applies the Rindler method to define and compute timelike entanglement entropy in Lorentzian theories.

Findings

Timelike entanglement entropy can be viewed as thermal entropy after Rindler transformation.

A gravitational dual for covariant timelike entanglement entropy is proposed.

The formula includes a constant term related to the central charge.

Abstract

For a Lorentzian invariant theory, the entanglement entropy should be a function of the domain of dependence of the subregion under consideration. More precisely, it should be a function of the domain of dependence and the appropriate cut-off. In this paper, we refine the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant $ic\pi/6$ with $c$ the central charge. The gravitational dual of the `covariant' timelike entanglement entropy is finally presented following this method.