Two-loop Integrability of Planar N=6 Superconformal Chern-Simons Theory

TL;DR

This paper proves the integrability of the complete planar two-loop dilatation generator in N=6 superconformal Chern-Simons theory, supporting the validity of Bethe ansatz equations for the spectral problem in AdS_4/CFT_3.

Contribution

It derives the full two-loop dilatation generator from superconformal symmetry and proves integrability in a sector, extending the understanding of spectral properties in the theory.

Findings

Complete two-loop dilatation generator derived from symmetry.

Integrability established in the osp(4|2) sector via Yangian construction.

Confirmation of Bethe ansatz applicability at weak coupling.

Abstract

Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS_4/CFT_3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the su(4) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of N=6 superconformal Chern-Simons theory from osp(6|4) superconformal symmetry. For the osp(4|2) sector, we prove integrability through a Yangian construction. We argue that integrability extends to the full planar two-loop dilatation generator, confirming the applicability of the Bethe equations at weak coupling. Further confirmation follows from an analytic computation of the two-loop twist-one spectrum.