Nonplanar integrability at two loops

Abstract

In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize the one loop dilatation operator are not corrected at two loops. The resulting spectrum of anomalous dimensions is related to a set of decoupled harmonic oscillators, indicating integrability in this sector of the theory at two loops. The anomalous dimensions are a non-trivial function of the 't Hooft coupling, with a spectrum that is continuous and starting at zero at large N, but discrete at finite N.

version to appear in JHEP

References in corpus (4)

• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Nonplanar Integrability
• Surprisingly Simple Spectra

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• Higher Loop Nonplanar Anomalous Dimensions from Symmetry
• Exciting LLM Geometries
• Relation between large dimension operators and oscillator algebra of Young diagrams
• SO(N) restricted Schur polynomials
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Restricted Schurs and correlators for SO(N) and Sp(N)
• Subleading corrections to the Double Coset Ansatz preserve integrability
• Interacting Double Coset Magnons
• Oscillating Multiple Giants
• Non-planar operator mixing by Brauer representations
• Heavy Operators in Superconformal Chern-Simons Theory
• Large N anomalous dimensions for large operators in Leigh-Strassler deformed SYM
• Counting paths with Schur transitions