From Large N Nonplanar Anomalous Dimensions to Open Spring Theory

Abstract

In this note we compute the non-planar one loop anomalous dimension of restricted Schur polynomials that have a bare dimension of O(N). This is achieved by mapping the restricted Schur polynomials into states of a specific U(N) irreducible representation. In this way the dilatation operator is mapped into a u(n) valued operator and, as a result, can easily be diagonalized. The resulting spectrum is reproduced by a classical model of springs between masses.

arXiv comment13+1 pages, 3 figures

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• A double coset ansatz for integrability in AdS/CFT
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• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Giant gravitons: a collective coordinate approach
• Restricted Schur Polynomials for Fermions and integrability in the su(2|3) sector
• Correlation functions and representation bases in free N=4 Super Yang-Mills
• Non-planar Anomalous Dimensions in the sl(2) Sector
• Operators, Correlators and Free Fermions for SO(N) and Sp(N)
• Open spin chains for giant gravitons and relativity
• A basis for large operators in N=4 SYM with orthogonal gauge group
• Nonplanar integrability at two loops
• Sketches of emergent geometry in the gauge/gravity duality
• BPS coherent states and localization
• Beyond the Planar Limit in ABJM
• Higher Loop Nonplanar Anomalous Dimensions from Symmetry
• Integrable Subsectors from Holography
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Relation between large dimension operators and oscillator algebra of Young diagrams
• SO(N) restricted Schur polynomials
• Central Charges for the Double Coset
• Restricted Schurs and correlators for SO(N) and Sp(N)
• Subleading corrections to the Double Coset Ansatz preserve integrability
• Nonplanar Integrability and Parity in ABJ Theory
• Orthogonal Schurs for Classical Gauge Groups
• Finite N Quiver Gauge Theory
• Graph duality as an instrument of Gauge-String correspondence
• Anomalous dimensions from boson lattice models
• Novel charges in CFT's
• Generating Functions for Giant Graviton Bound States
• Interacting Double Coset Magnons
• Oscillating Multiple Giants
• Non-planar operator mixing by Brauer representations
• Heavy Operators in Superconformal Chern-Simons Theory
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
• Interacting Emergent Yang-Mills theory
• Large N anomalous dimensions for large operators in Leigh-Strassler deformed SYM
• Counting paths with Schur transitions