Integrable subsectors from holography

Abstract We consider operators in N=4 $$ \mathcal{N}=4 $$ super Yang-Mills theory dual to closed string states propagating on a class of LLM geometries. The LLM geometries we consider are specified by a boundary condition that is a set of black rings on the LLM plane. When projected to the LLM plane, the closed strings are polygons with all corners lying on the outer edge of a single ring. The large N limit of correlators of these operators receives contributions from non-planar diagrams even for the leading large N dynamics. Our interest in these fluctuations is because a previous weak coupling analysis argues that the net effect of summing the huge set of non-planar diagrams, is a simple rescaling of the ’t Hooft coupling. We carry out some nontrivial checks of this proposal. Using the su(2|2)2 symmetry we determine the two magnon S-matrix and demonstrate that it agrees, up to two loops, with a weak coupling computation performed in the CFT. We also compute the first finite size corrections to both the magnon and the dyonic magnon by constructing solutions to the Nambu-Goto action that carry finite angular momentum. These finite size computations constitute a strong coupling confirmation of the proposal.