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We show that all IIB backgrounds with strictly 28 supersymmetries are locallyisometric to the plane wave solution of arXiv:hep-th/0206195. Moreover, wedemonstrate that all solutions with more than 26 supersymmetries and only5-form flux are maximally supersymmetric. The N=28 plane wave solution is asuperposition of the maximally supersymmetric IIB plane wave with a heteroticstring solution. We investigate the propagation of strings in this background,find the spectrum and give the string light-cone Hamiltonian.

Classification of IIB backgrounds with 28 supersymmetries