Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM

Abstract

We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as determinant of a semi-infinite matrix. We find that at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients and give the full perturbative expansion of the octagon.

arXiv comment5 pages, 1 figure

References in corpus (19)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Review of AdS/CFT Integrability: An Overview
• Quantum spectral curve for AdS_5/CFT_4
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Hexagonalization of Correlation Functions
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Tessellating cushions: four-point functions in N=4 SYM
• Gluing Ladders into Fishnets
• Correlation functions for symmetrized increasing subsequences
• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Clustering and the Three-Point Function
• Handling Handles. Part II. Stratification and Data Analysis
• Asymptotic Four Point Functions
• A Note on the Pfaffian Integration Theorem

Cited by in corpus (36)

• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Ten dimensional symmetry of N=4 SYM correlators
• Exact null octagon
• 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
• Exactly solvable magnet of conformal spins in four dimensions
• Octagons I: Combinatorics and Non-Planar Resummations
• The Octagon as a Determinant
• Crossing bridges with strong Szego limit theorem
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Two-particle spectrum of tensor multiplets coupled to $Ad{S}_3\times S^3$ gravity
• Decagon at Two Loops
• An Operator Product Expansion for Form Factors III. Finite Coupling and Multi-Particle Contributions
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Functional Equations and Separation of Variables for Exact g-Function
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Effective Quantum Field Theory for the Thermodynamical Bethe Ansatz
• Octagons II: Strong Coupling
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• Octagon with finite bridge: free fermions and determinant identities
• Three-point functions at strong coupling in the BMN limit
• $Ad{S}_5\times S^5$ supergravity vertex operators
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Separation of Variables for a flux tube with an end
• Exploring superconformal Yang-Mills theories through matrix Bessel kernels
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Loop Equation and Exact Soft Anomalous Dimension in N=4 Super Yang-Mills
• 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