An alternative S-matrix for N=6 Chern-Simons theory ?

TL;DR

The paper investigates whether a non-reflectionless, integrable S-matrix could be consistent with perturbative BAEs for the planar $N=6$ ABJM theory. It constructs a tensor-product S-matrix with a flavor SU(2) part and derives the all-loop BAEs via the Bethe-Yang transfer-matrix method, analyzing the weak-coupling limit. The resulting BAEs fail to reproduce the two-loop BAEs of Minahan and Zarembo, lacking the expected node structure, and are thus not viable. This finding strengthens confidence in the original reflectionless S-matrix proposed by Ahn and Nepomechie and the associated Gromov–Vieira all-loop BAEs, with additional support from other consistency checks for ABJM integrability.

Abstract

We have recently proposed an S-matrix for the planar limit of the N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena which leads to the all-loop Bethe ansatz equations conjectured by Gromov and Vieira. An unusual feature of this proposal is that the scattering of A and B particles is reflectionless. We consider here an alternative S-matrix, for which A-B scattering is not reflectionless. We argue that this S-matrix does not lead to the Bethe ansatz equations which are consistent with perturbative computations.