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

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.

References in corpus (10)

• Left-Right Entanglement Entropy of Boundary States
• A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
• String spectra near some null cosmological singularities
• D-branes as coherent states in the open string channel
• Strings in Horizons, Dissipation and a Possible Interpretation of the Hagedorn Temperature
• String Entanglement and D-branes as Pure States
• Entanglement and entropy operator for strings in pp-wave time dependent background
• Observer dependent D-brane for strings propagating in pp-wave time dependent background
• Excited states of a string in a time dependent orbifold
• Tachyon - Dilaton driven Inflation as an alpha' - non-perturbative solution in First Quantized String Cosmology

Cited by in corpus (2)

• LREE of a Dressed D$p$-brane with Transverse Motion in the Partially Compact Spacetime
• On the Hagedorn behavior of the superstring propating in a cosmological time dependent background