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arXiv · hep-th/0304198

Solvable models of strings in homogeneous plane wave backgrounds

Matthias Blau·Martin O'Loughlin·George Papadopoulos·Arkady A. Tseytlin
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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.

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Matthias Blau, Martin O'Loughlin, George Papadopoulos, Arkady A. Tseytlin. 2003-06-10. Solvable models of strings in homogeneous plane wave backgrounds. https://doi.org/10.1016/j.nuclphysb.2003.09.018

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