The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory

TL;DR

This work analyzes the string dual of ABJM theory in the $SU(2)\times SU(2)$ sector, deriving a two-Landau-Lifshitz sigma-model limit, a Penrose limit that yields a magnon dispersion, and a novel Giant Magnon solution. The results produce a coupling-dependent magnon dispersion $\Delta = \sqrt{\tfrac{1}{4} + h(\lambda) \sin^2(\tfrac{p}{2})}$, with $h(\lambda)$ interpolating between $h(\lambda)\sim 4\lambda^2$ at weak coupling and $h(\lambda)\sim 4\lambda$ at strong coupling, consistent with both LL-type dynamics and pp-wave analysis. The analysis highlights differences from the $AdS_5$/CFT$_4$ case due to reduced supersymmetry and suggests rich integrable structure in ABJM, including cross-regime consistency and avenues for further study of the S-matrix and finite-size effects. Overall, the paper connects weak- and strong-coupling descriptions of the $SU(2)\times SU(2)$ sector through explicit sigma-model, Penrose, and Giant Magnon constructions in type IIA string theory on $AdS_4\times\mathbb{CP}^3$.

Abstract

We examine the string dual of the recently constructed $\mathcal{N}=6$ superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the $SU(2)\times SU(2)$ sector. We find a sigma-model limit in which the resulting sigma-model is two Landau-Lifshitz models added together. We consider a Penrose limit for which we can approach the $SU(2)\times SU(2)$ sector. Finally, we find a new Giant Magnon solution in the $SU(2)\times SU(2)$ sector corresponding to one magnon in each $SU(2)$. We put these results together to find the full magnon dispersion relation and we compare this to recently found results for ABJM theory at weak coupling.