Plane-wave matrix theory from super-Yang–Mills on

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.