Entanglement and entropy operator for strings in pp-wave time dependent background

TL;DR

This paper investigates string behavior in a time-dependent pp-wave background with a null singularity, revealing dynamically generated entanglement entropy and implications for observer-dependent vacuum states and information loss.

Contribution

It introduces a new analysis of entanglement entropy and vacuum inequivalence in string theory within a time-dependent background with a null singularity.

Findings

Entanglement entropy diverges near the singularity.

Vacuum states are unitarily inequivalent at different times.

Finite-time vacuum appears thermal to stationary observers.

Abstract

In this letter new aspects of string theory propagating in a pp-wave time dependent background with a null singularity are explored. It is shown the appearance of a 2d entanglement entropy dynamically generated by the background. For asymptotically flat observers, the vacuum close to the singularity is unitarily inequivalent to the vacuum at $\tau = -\infty$ and it is shown that the 2d entanglement entropy diverges close to this point. As a consequence, the positive time region is inaccessible for observers in $\tau =-\infty$. For a stationary measure, the vacuum at finite time is seen by those observers as a thermal state and the information loss is encoded as a heat bath of string states.