Octagons I: Combinatorics and Non-Planar Resummations

Abstract

We explain how the 't Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in N=4 super Yang-Mills theory. The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the 't Hooft coupling and spacetime dependence. At each genus g in the large Nc expansion, this function is a polynomial of degree 2g+2 in the octagon. We find several dual matrix model representations of the correlators in the large-charge limit. Amusingly, the number of colors in these matrix models is formally taken to zero in the relevant limit.

arXiv comment22+26 pages, 29 figures; v2: references updated, small changes and additions, published version

References in corpus (41)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Combinatorics of Boundaries in String Theory
• A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings
• PP-wave string interactions from perturbative Yang-Mills theory
• BMN Correlators and Operator Mixing in N=4 Super Yang-Mills Theory
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Diagonal multi-matrix correlators and BPS operators in N=4 SYM
• Hexagonalization of Correlation Functions
• Operator Mixing and the BMN Correspondence
• Characteristic polynomials of random matrices
• Tessellating cushions: four-point functions in N=4 SYM
• Character Expansion Methods for Matrix Models of Dually Weighted Graphs
• BMN Gauge Theory as a Quantum Mechanical System
• On correlation functions of operators dual to classical spinning string states
• Exact vs. Semiclassical Target Space of the Minimal String
• Gluing Ladders into Fishnets
• On the complete perturbative solution of one-matrix models
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Exact Solution of Discrete Two-Dimensional R^2 Gravity
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Rectangular Matrix Models and Combinatorics of Colored Graphs
• A Generating Function for Fatgraphs
• A light-cone approach to three-point functions in AdS_5 x S^5
• The Holographic Fishchain
• Intersection theory from duality and replica
• Handling Handles. Part II. Stratification and Data Analysis
• Holographic three-point functions for short operators
• Vertices from replica in a random matrix theory
• Computing Three-Point Functions for Short Operators
• Almost Flat Planar Diagrams
• Two-Dimensional Chiral Matrix Models and String Theories
• Space-like minimal surfaces in AdS x S
• Complex matrix model duality
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Duality and replicas for a unitary matrix model
• Octagons II: Strong Coupling
• Field Theory as a Matrix Model

Cited by in corpus (30)

• One-loop amplitudes in $Ad{S}_5\times S^5$ supergravity from $\mathcal{N}=4$ SYM at strong coupling
• Ten dimensional symmetry of N=4 SYM correlators
• Octagon at finite coupling
• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings
• Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• The Octagon as a Determinant
• Crossing bridges with strong Szego limit theorem
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Non-planar data of $\mathcal{N}=4$ SYM
• The OPE meets semiclassics
• Decagon at Two Loops
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz
• On three-point functions in ABJM and the latitude Wilson loop
• Octagons II: Strong Coupling
• Octagon with finite bridge: free fermions and determinant identities
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Light-cone limits of large rectangular fishnets
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Three-Point Functions in ABJM and Bethe Ansatz
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons