Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond

TL;DR

This paper investigates the perturbative integrability of N=6 Chern-Simons theory at six loops, deriving interactions, analyzing operator mixing, and confirming spectrum predictions consistent with quantum integrability.

Contribution

It provides a detailed six-loop analysis of the spectrum and operator mixing in N=6 Chern-Simons theory, confirming integrability predictions and extending previous lower-loop results.

Findings

Spectrum matches integrability predictions up to six loops

Homogeneous diagrams are recursively obtainable to all orders

Only one operator combination contributes, same as in N=4 super Yang-Mills

Abstract

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. These diagrams require proper regularization of not only ultraviolet but also infrared divergences. We first consider 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 spectrum of the quantum dilatation generator up to six loop orders. 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. We then study 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 remarkable integer-relation algorithm (PSLQ) developed by Ferguson, Baily and Arno.