Integrability of N=6 Chern-Simons theory at six loops and beyond

We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak t'Hooft coupling regime. By Feynman diagrammatics, we derive so-called maximal-ranged interactions in the quantum dilatation generator, originating from homogeneous and inhomogeneous diagrams. The dilatation operator requires proper regularization of ultraviolet and infrared divergences and also bears scheme dependence depending on operator-mixing or two-point function methods adopted. We first consider the standard operator-mixing method. We show that homogeneous diagrams are obtainable by recursive method to all orders. The method, however, is not easily extendable to inhomogeneous diagrams. We thus consider two-point function method and study both operator contents and the spectrum of the quantum dilatation generator up to six-loop orders. Within this scheme, we show that, of two possible classes of operators, only one linear combination actually contributes. Curiously, this is exactly the same combination as in N=4 super Yang-Mills theory. From these operators, we extract a spectrum of anomalous dimension up to six loops. We find that the spectrum agrees perfectly with the prediction based on quantum integrability. In evaluating the six-loop diagrams, we utilized a remarkable integer-relation algorithm developed by Ferguson, Baily, and Arno.