Two-loop integrability of planar superconformal Chern–Simons theory

Abstract

Bethe ansatz equations have been proposed for the asymptotic spectral problem of AdS4/CFT3. This proposal assumes integrability, but the previous verification of weak-coupling integrability covered only the sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of superconformal Chern–Simons theory from superconformal symmetry. For the 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.