Nonplanar Integrability

Abstract

In this article we study operators with a dimension $\Delta \sim O(N)$ and show that simple analytic expressions for the action of the dilatation operator can be found. The operators we consider are restricted Schur polynomials. There are two distinct classes of operators that we consider: operators labeled by Young diagrams with two long columns or two long rows. The main complication in working with restricted Schur polynomials is in building a projector from a given $S_{n+m}$ irreducible representation to an $S_n\times S_m$ irreducible representation (both specified by the labels of the restricted Schur polynomial). We give an explicit construction of these projectors by reducing it to the simple problem of addition of angular momentum in ordinary non-relativistic quantum mechanics. The diagonalizationof the dilatation operator reduces to solving three term recursion relations. The fact that the recursion relations have only three terms is a direct consequence of the weak mixing at one loop of the restricted Schur polynomials. The recursion relations can be solved exactly in terms of symmetric Kravchuk polynomials or in terms of Clebsch-Gordan coefficients. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable.

1+51 pages, 3 figures, v2: typos fixed

References in corpus (52)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Dielectric-Branes
• Bubbling AdS space and 1/2 BPS geometries
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Giant Gravitons in Conformal Field Theory
• Large branes in AdS and their field theory dual
• A toy model for the AdS/CFT correspondence
• SUSY and Goliath
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• The Library of Babel: On the origin of gravitational thermodynamics
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Exact Multi-Matrix Correlators
• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Large N BPS states and emergent quantum gravity
• D-branes in Yang-Mills theory and Emergent Gauge Symmetry
• AdS(3) Solutions of IIB Supergravity from D3-branes
• Supersymmetric states of N=4 Yang-Mills from giant gravitons
• Diagonal free field matrix correlators, global symmetries and giant gravitons
• Supersymmetric AdS_3, AdS_2 and Bubble Solutions
• Giant Gravitons - with Strings Attached (III)
• Fermions from Half-BPS Supergravity
• Giant Gravitons - with Strings Attached (II)
• Exact Multi-Restricted Schur Polynomial Correlators
• Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• Finite Factorization equations and Sum Rules for BPS correlators in N=4 SYM theory
• Enhanced symmetries of gauge theory and resolving the spectrum of local operators
• Counting 1/8-BPS Dual-Giants
• The Library of Babel
• Geometries from Young Diagrams
• BPS Geometries and AdS Bubbles
• Surprisingly Simple Spectra
• Entropy of near-extremal black holes in AdS_5
• Brane webs and 1/4-BPS geometries
• Nearing Extremal Intersecting Giants and New Decoupled Sectors in N = 4 SYM
• A description of 1/4 BPS configurations in minimal type IIB SUGRA
• From counting to construction of BPS states in N=4 SYM
• Schur-Weyl duality as an instrument of Gauge-String duality
• Emergent Threebrane Lattices
• Permutations and the Loop
• 1/8 BPS States in Ads/CFT
• Correlators in Nontrivial Backgrounds
• Geometry and topology of bubble solutions from gauge theory
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Quarter BPS classified by Brauer algebra
• Correlators Of Operators with a Large R-charge
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• Strings on Bubbling Geometries
• Studies on 1/4 BPS and 1/8 BPS geometries

Cited by in corpus (73)

• Giant Graviton Oscillators
• Holographic three-point functions of giant gravitons
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• A double coset ansatz for integrability in AdS/CFT
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• On Marginal Deformations and Non-Integrability
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Giant gravitons: a collective coordinate approach
• Non-integrability in non-relativistic theories
• From Large N Nonplanar Anomalous Dimensions to Open Spring Theory
• Emergent IR dual 2d CFTs in charged AdS5 black holes
• Restricted Schur Polynomials for Fermions and integrability in the su(2|3) sector
• Non-planar Anomalous Dimensions in the sl(2) Sector
• Correlation functions and representation bases in free N=4 Super Yang-Mills
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Permutation Centralizer Algebras and Multi-Matrix Invariants
• Operators, Correlators and Free Fermions for SO(N) and Sp(N)
• A basis for large operators in N=4 SYM with orthogonal gauge group
• Analytic integrability for strings on $\eta$ and $\lambda$ deformed backgrounds
• Nonplanar integrability at two loops
• The giant graviton on AdS_{4} x CP^{3} - another step towards the emergence of geometry
• Interacting Giant Gravitons from Spin Matrix Theory
• LLM Magnons
• Positivity of hexagon perturbation theory
• Beyond the Planar Limit in ABJM
• Higher Loop Nonplanar Anomalous Dimensions from Symmetry
• The Panorama of Spin Matrix Theory
• ABJM Dibaryon Spectroscopy
• Detecting topology change via correlations and entanglement from gauge/gravity correspondence
• Exciting LLM Geometries
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Multi-matrix models and Noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras
• Flavour singlets in gauge theory as Permutations
• Integrable Subsectors from Holography
• Quantum states to brane geometries via fuzzy moduli spaces of giant gravitons
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• SO(N) restricted Schur polynomials
• Central Charges for the Double Coset
• Relation between large dimension operators and oscillator algebra of Young diagrams
• Scrambling in Yang-Mills
• Emergent Yang-Mills theory
• Young diagrams, Brauer algebras, and bubbling geometries
• Negative anomalous dimensions in N=4 SYM
• Restricted Schurs and correlators for SO(N) and Sp(N)
• Subleading corrections to the Double Coset Ansatz preserve integrability
• A giant graviton genealogy
• Nonplanar Integrability and Parity in ABJ Theory
• New results for the SQCD Hilbert series
• Orthogonal Schurs for Classical Gauge Groups
• Graph duality as an instrument of Gauge-String correspondence
• Finite N Quiver Gauge Theory
• Novel charges in CFT's
• Anomalous dimensions from boson lattice models
• Generating Functions for Giant Graviton Bound States
• Interior analysis, stretched technique and bubbling geometries
• From Gauss Graphs to Giants
• Interacting Double Coset Magnons
• Oscillating Multiple Giants
• Correlation functions of determinant operators in conformal fishnet theory
• Non-planar operator mixing by Brauer representations
• Analytic (non)integrability of Arutyunov-Bassi-Lacroix model
• Rotating Restricted Schur Polynomials
• 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
• Generalised cusp anomalous dimension in beta-deformed super Yang Mills theory
• Counting paths with Schur transitions
• Splitting of Folded Strings in AdS_4*CP^3
• Entanglement and mixed states of Young tableau states in gauge/gravity correspondence