Two-loop integrability of planar \({\mathcal N}=6\) superconformal Chern-Simons theory. (English) Zbl 1179.81143
Summary: 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 \(\mathfrak{su}(4) \) sector of the ABJM gauge theory. Here we derive the complete planar two-loop dilatation generator of \({\mathcal N}=6 \) superconformal Chern-Simons theory from \(\mathfrak{osp}(6|4) \) superconformal symmetry. For the \(\mathfrak{osp}(4|2) \) 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.
MSC:
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
81T10 | Model quantum field theories |
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
81T13 | Yang-Mills and other gauge theories in quantum field theory |
81V15 | Weak interaction in quantum theory |
81R12 | Groups and algebras in quantum theory and relations with integrable systems |