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

We examine the string dual of the recently constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the SU(2)×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)×SU(2) sector. Finally, we find a new Giant Magnon solution in the SU(2)×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.