Exactly Solvable Model of Superstring in Plane-wave Background with Linear Null Dilaton

TL;DR

This work analyzes an exactly solvable IIB superstring in a time-dependent plane-wave background with a linear null dilaton and constant self-dual RR 5-form flux, preserving 16 supersymmetries. In the light-cone gauge, the worldsheet theory reduces to free 2D bosons and fermions with time-dependent masses, and the total Hamiltonian is time-dependent with a vanishing zero-point energy due to boson–fermion cancellation. The bosonic and fermionic spectra are symmetric, and quantum string mode creation is found to be negligible, even near a cosmological singularity where the string coupling is strong. The authors derive explicit mode expansions, diagonalize the light-cone Hamiltonian via time-dependent Bogoliubov-type transformations, and discuss implications for string dynamics and potential nonperturbative descriptions in the strong-coupling regime.

Abstract

In this paper, we study an exactly solvable model of IIB superstring in a time-dependent plane-wave backgound with a constant self-dual Ramond-Ramond 5-form field strength and a linear dilaton in the light-like direction. This background keeps sixteen supersymmetries. In the light-cone gauge, the action is described by the two-dimensional free bosons and fermions with time-dependent masses. The model could be canonically quantized and its Hamiltonian is time-dependent with vanishing zero point energy. The spectrum of the excitations is symmetric between the bosonic and fermionic sector. The string mode creation turns out to be very small.