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We study a new class of inhomogeneous pp-wave solutions with 8 unbrokensupersymmetries in D=11 supergravity. The 9 dimensional transverse space isEuclidean and split into 3 and 6 dimensional subspaces. The solutions havenon-constant gauge flux, which are described in terms of an arbitraryholomorphic function of the complexified 6 dimensional space. The supermembraneand matrix theory descriptions are also provided and we identify the relevantsupersymmetry transformation rules. The action also arises through adimensional reduction of N=1, D=4 supersymmetric Yang-Mills theory coupled to 3gauge adjoint and chiral multiplets, whose interactions are determined by theholomorphic function of the supergravity solution now constituting thesuperpotential.

M-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions