Bootstrapping the simplest correlator in planar N = 4 SYM at all loops

Abstract

We present the full form of a four-point correlation function of large BPS operators in planar N = 4 Super Yang-Mills to any loop order. We do this by following a bootstrap philosophy based on three simple axioms pertaining to (i) the space of functions arising at each loop order, (ii) the behaviour in the OPE in a double-trace dominated channel and (iii) the behaviour under a double null limit. We discuss how these bootstrap axioms are in turn strongly motivated by empirical observations up to nine loops unveiled through integrability methods in our previous work [9] on this simplest correlation function.

arXiv comment5 pages, 2 figures

References in corpus (27)

• Transcendentality and Crossing
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Mellin amplitudes for $Ad{S}_5\times S^5$
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• How to Succeed at Holographic Correlators Without Really Trying
• Heptagons from the Steinmann Cluster Bootstrap
• Gravitational S-matrix from CFT dispersion relations
• Loop Corrections to Supergravity on $Ad{S}_5\times S^5$
• From correlation functions to Wilson loops
• Hexagonalization of Correlation Functions
• All Tree-Level Correlators in AdS${}_5\times$S${}_5$ Supergravity: Hidden Ten-Dimensional Conformal Symmetry
• Tessellating cushions: four-point functions in N=4 SYM
• Higher-spin correlators
• Gluing Ladders into Fishnets
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Genus-One String Amplitudes from Conformal Field Theory
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• All three-loop four-point correlators of half-BPS operators in planar N=4 SYM
• Exact Correlation Functions in Conformal Fishnet Theory
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Handling Handles. Part II. Stratification and Data Analysis
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Bootstrapping correlation functions in N=4 SYM
• Crossing symmetry and Higher spin towers

Cited by in corpus (44)

• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Ten dimensional symmetry of N=4 SYM correlators
• Exact null octagon
• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• 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
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Crossing bridges with strong Szego limit theorem
• Bootstrapping $\mathcal{N}=4$ sYM correlators using integrability
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Strong coupling expansions in $\mathcal{N}=2$ quiver gauge theories
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Mirror channel eigenvectors of the $d$-dimensional fishnets
• Decagon at Two Loops
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Yangian Ward Identities for Fishnet Four-Point Integrals
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Hexagonalization of Fishnet integrals I: mirror excitations
• Yangian Symmetry in Holographic Correlators
• Octagons II: Strong Coupling
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• Octagon with finite bridge: free fermions and determinant identities
• $Ad{S}_5\times S^5$ supergravity vertex operators
• An Origin Story for Amplitudes
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Spinning Hexagons
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• Separation of Variables for a flux tube with an end
• Light-cone limits of large rectangular fishnets
• Antipodal self-duality of square fishnet graphs
• Bethe Ansatz for Quantum-Deformed Strings
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Higher-Point Correlators in N=4 SYM: Generating Functions
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons