  Recently a mass deformation of the maximally supersymmetric Yang-Mills
quantum mechanics has been constructed from the supermembrane action in eleven
dimensional plane-wave backgrounds. However, the origin of this plane-wave
matrix theory in terms of a compactification of a higher dimensional Super
Yang-Mills model has remained obscure. In this paper we study the Kaluza-Klein
reduction of D=4, N=4 Super Yang-Mills theory on a round three-sphere, and
demonstrate that the plane-wave matrix theory arises through a consistent
truncation to the lowest lying modes. We further explore the relation between
the dilatation operator of the conformal field theory and the hamiltonian of
the quantum mechanics through perturbative calculations up to two-loop order.
In particular we find that the one-loop anomalous dimensions of pure scalar
operators are completely captured by the plane-wave matrix theory. At two-loop
level this property ceases to exist.
