Matrix Strings in pp-wave backgrounds from deformed Super Yang-Mills Theory

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We formulate matrix models for strings in ten dimensional pp-wave backgrounds and for particles in eleven dimensional ones. This is done by first characterizing the deformations of ten dimensional N=1 SYM which are induced by a constant bispinorial coupling ∫ ΨHΨ plus a minimal purely bosonic completition and then by the appropriate dimensional reduction. We find a whole class of new models for the matrix strings and a generalization of the supernumerary supersymmetric models as far as the matrix theory for particles is concerned. A companion deformation of the IKKT matrix model is also discussed.