Observer dependent D-brane for strings propagating in pp-wave time dependent background

TL;DR

This paper investigates type IIB superstrings in a time-dependent pp-wave background with a singularity, revealing observer-dependent D-brane descriptions and constructing a Bogoliubov transformation linking different Hilbert spaces.

Contribution

It introduces a unitary Bogoliubov generator that relates asymptotic and finite-time string Hilbert spaces in a singular background, highlighting observer-dependent vacuum states.

Findings

Asymptotically flat observers see the vacuum as a boundary state D-brane.

Observers near the singularity perceive the original vacuum.

The model provides insights into black hole horizon and complementarity concepts.

Abstract

We study type IIB superstring in the pp-wave time-dependent background, which has a singularity at $t=0$. We show that this background can provide a toy model to study some ideas related to the stretched horizon paradigm and the complementary principle of black holes. To this end, we construct a unitary Bogoliubov generator which relates the asymptotically flat string Hilbert space, defined at $t =\pm \infty$, to the finite time Hilbert space. For asymptotically flat observers, the closed string vacuum close to the singularity appears as a boundary state which is in fact a D-brane described in the closed string channel. However, observers who go with the string towards to the singularity see the original vacuum.