Integrable Subsectors from Holography

TL;DR

This paper investigates operators in ${ m extbf{N}=4}$ super Yang-Mills theory dual to string states in specific LLM geometries, providing strong and weak coupling analyses that support a simplified rescaling of the 't Hooft coupling due to non-planar diagram contributions.

Contribution

It offers a detailed comparison of weak and strong coupling results for string excitations in LLM geometries, confirming a proposed rescaling of the 't Hooft coupling at large N.

Findings

Agreement of the $su(2|2)^2$ $S$-matrix with two-loop weak coupling calculations

Finite size corrections match strong coupling Nambu-Goto solutions

Non-planar diagrams contribute significantly even at large N

Abstract

We consider operators in ${\cal N}=4$ 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.