Cluster adjacency and the four-loop NMHV heptagon

Abstract

We exploit the recently described property of cluster adjacency for scattering amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory to construct the symbol of the four-loop NMHV heptagon amplitude. We use a manifestly cluster adjacent ansatz and describe how the parameters of this ansatz are determined using simple physical consistency requirements. We then specialise our answer for the amplitude to the multi-Regge limit, finding agreement with previously available results up to the next-to-leading logarithm, and obtaining new predictions up to (next-to)${}^3$-leading-logarithmic accuracy.

arXiv comment29 pages; v2: published version, typos corrected, symbol bases up to weight 6 included as ancillary files

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• A Three-Point Form Factor Through Five Loops
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• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
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• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Antipodal Self-Duality for a Four-Particle Form Factor
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
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• Notes on cluster algebras and some all-loop Feynman integrals
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• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Schubert Problems, Positivity and Symbol Letters
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• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
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• Bootstrapping a Two-Loop Four-Point Form Factor
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• Intersection theory rules symbology
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• An Infinite Family of Elliptic Ladder Integrals
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• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• A Two-Loop Four-Point Form Factor at Function Level
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• Exploring Reggeon bound states in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Hexagon Bootstrap in the Double Scaling Limit