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) × 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 wellbehaved. 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.

Quantization of Open strings in time dependent Black Holes

“…In [6] it was studied a model that admits a pre-Big Bang phase scenario and it was argued that the string passes through the null singular point. In [7] it was shown that the left/right entanglement entropy of the Green-Schwarz superstring is finite in the cosmological singularity of the background and hence it is a good measure to explore string theory near singularities. In addition, it was shown that the time dependent left/right closed string entropy has an equilibrium point close to the singularity and, actually at the singularity, it is equal to the thermodynamic entropy of an open string.…”