Integrable Subsectors from Holography

Abstract

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

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References in corpus (14)

• Giant Magnons
• Finite-size Effects from Giant Magnons
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Nonplanar Integrability
• Giant Gravitons - with Strings Attached (III)
• Giant Gravitons - with Strings Attached (II)
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Finite-Size Effects for Dyonic Giant Magnons
• Surprisingly Simple Spectra
• Permutations and the Loop
• Code subspaces for LLM geometries

Cited by in corpus (11)

• Positivity of hexagon perturbation theory
• Maximally Supersymmetric RG Flows in 4D and Integrability
• Exciting LLM Geometries
• Quarter-BPS states, multi-symmetric functions and set partitions
• Non-Perturbative String Theory from AdS/CFT
• Semiclassical SL(2) Strings on LLM backgrounds
• Interior analysis, stretched technique and bubbling geometries
• Oscillating Multiple Giants
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Correlation functions of determinant operators in conformal fishnet theory
• Three-Point Functions in ABJM and Bethe Ansatz