Left/right entanglement and thermalization of time dependent plane wave Green-Schwarz superstring

TL;DR

This paper investigates the behavior of type IIB superstrings in a time-dependent plane wave background, revealing how entanglement entropy evolves and indicating thermalization near singularities, with implications for string theory in dynamic spacetimes.

Contribution

It introduces a unitary Bogoliubov transformation for superstrings in a time-dependent background and analyzes entanglement and thermalization near singularities.

Findings

Entanglement entropy remains well-behaved near the null singularity.

The superstring vacuum appears as a thermal state close to the singularity.

Superstring thermalization occurs, with entropy resembling thermodynamic entropy.

Abstract

In this work we study new issues involving the type IIB superstring in a time dependent plane wave background with a constant self-dual Ramond-Ramond 5-form and a linear dilaton in the light-like direction. We construct a unitary Bogoliubov generator which relates the asymptotically flat superstring Hilbert space to the finite time Hilbert space. The time dependent vacuum is a superposition of $SU(1, 1)\times SU(2)$ coherent states, which has a particular structure of excitation, characterized by a condensation of right and left moving supertring modes. We calculate the time dependent left/right entanglement entropy and carry out the summation over the oscillator modes of the superstring two-point function. We show that, close to the null singularity, the entanglement entropy is well-behaved. In particular, for asymptotically flat observers, the closed superstring vacuum close to the singularity appears as superstring thermal vacuum, which is unitarily inequivalent to the asymptotically flat vacuum. Actually, we show that close to the singularity the superstring thermalizes and the entanglement entropy becomes a thermodynamical entropy for a supersymmetric two-dimensional gas.