Solvable models of strings in homogeneous plane wave backgrounds

TL;DR

This paper provides exact solutions for string theory in a broad class of homogeneous plane wave backgrounds, revealing novel spectral features and stability properties influenced by background parameters.

Contribution

It introduces a general method for solving string equations in these backgrounds and analyzes the resulting spectra, including new phenomena like massless states and mode stabilization.

Findings

Discovery of new massless states at non-zero levels

Stabilization of tachyonic modes by background parameters

Unusual spectral features such as non-positive definite oscillator spectra

Abstract

We solve closed string theory in all regular homogeneous plane-wave backgrounds with homogeneous NS three-form field strength and a dilaton. The parameters of the model are constant symmetric and anti-symmetric matrices k_{ij} and f_{ij} associated with the metric, and a constant anti-symmetric matrix h_{ij} associated with the NS field strength. In the light-cone gauge the rotation parameters f_{ij} have a natural interpretation as a constant magnetic field. This is a generalisation of the standard Landau problem with oscillator energies now being non-trivial functions of the parameters f_{ij} and k_{ij}. We develop a general procedure for solving linear but non-diagonal equations for string coordinates, and determine the corresponding oscillator frequencies, the light-cone Hamiltonian and level matching condition. We investigate the resulting string spectrum in detail in the four-dimensional case and compare the results with previously studied examples. Throughout we will find that the presence of the rotation parameter f_{ij} can lead to certain unusual and unexpected features of the string spectrum like new massless states at non-zero string levels, stabilisation of otherwise unstable (tachyonic) modes, and discrete but not positive definite string oscillator spectra.