Abstract
In this article we consider gauge theories with a U(N)×U(N) gauge group. We provide, for the first time, a complete set of operators built from scalar fields that are in the bi-fundamental of the two groups. Our operators diagonalize the two point function of the free field theory at all orders in 1/N. We then use this basis to investigate non-planar anomalous dimensions in the ABJM theory. We show that the dilatation operator reduces to a set of decoupled harmonic oscillators, signaling integrability in a large N but non-planar limit of the theory.