N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations

TL;DR

The paper addresses the problem of obtaining an exact planar S-matrix for the $\mathcal{N}=6$ Chern-Simons (ABJM) theory in AdS$_4$/CFT$_3$ and deriving all-loop Bethe ansatz equations. It adopts a factorized S-matrix with $SU(2|2)$ symmetry for A- and B-type excitations, introducing two dressing phases related by crossing and incorporating the BES dressing factor $\sigma$. From this S-matrix, the authors formulate the asymptotic Bethe ansatz and show that the resulting Bethe-Yang equations reproduce the all-loop BAEs conjectured by Gromov and Vieira, validating the proposed integrable structure. The work also outlines future checks, including perturbative expansions, classical limits, and finite-size corrections, which could further confirm the link between the coupling $g$ and the ’t Hooft parameter $\lambda$ and illuminate the bound-state spectrum across the dualities.

Abstract

We propose the exact S-matrix for the planar limit of the N=6 super Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe ansatz equations confirms the all-loop Bethe ansatz equations recently conjectured by Gromov and Vieira.