Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin

Abstract

We initiate an exploration of the conformal bootstrap for $n>4$ point correlation functions. Here we bootstrap correlation functions of the lightest scalar gauge invariant operators in planar non-abelian conformal gauge theories as their locations approach the cusps of a null polygon. For that we consider consistency of the OPE in the so-called snowflake channel with respect to cyclicity transformations which leave the null configuration invariant. For general non-abelian gauge theories this allows us to strongly constrain the OPE structure constants of up to three large spin $J_j$ operators (and large polarization quantum number $l_j$) to all loop orders. In $\mathcal{N}=4$ we fix them completely through the duality to null polygonal Wilson loops and the recent origin limit of the hexagon explored by Basso, Dixon and Papathanasiou.

arXiv comment8 pages, 4 figures, 1 table and 2 mathematica notebooks. Typos corrected

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Cited by in corpus (27)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• OPE statistics from higher-point crossing
• Lightcone Bootstrap at higher points
• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Recursion relations for 5-point conformal blocks
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• The Wilson Loop -- Large Spin OPE Dictionary
• Shadow Celestial Amplitude
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Improving the five-point bootstrap
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Stampedes I: Fishnet OPE and Octagon Bootstrap with Nonzero Bridges
• An Origin Story for Amplitudes
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Spinning Hexagons
• Three twist-two, two spins, two loops
• Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary
• Sparsity in the numerical six-point bootstrap
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Spinors and conformal correlators
• Two spinning Konishi operators at three loops
• Five-point partial waves, splitting constraints and hidden zeros
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons