Solvable models of strings in homogeneous plane-wave backgrounds

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 antisymmetric matrix h(ij) associated with the NS field strength. In the light-cone gauge the rotation parameters fij 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. (C) 2003 Elsevier B.V. All rights reserved.