Hedgehog Bases for A_n Cluster Polylogarithms and An Application to Six-Point Amplitudes

Abstract

Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the $A_n$ cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

32 pages; v2: minor corrections and clarifications

References in corpus (9)

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• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
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Cited by in corpus (15)

• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Evidence for a Nonplanar Amplituhedron
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Prescriptive Unitarity
• Cluster algebras for Feynman integrals
• Rationalizing Loop Integration
• Gravity On-shell Diagrams
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Implications of nonplanar dual conformal symmetry
• Notes on cluster algebras and some all-loop Feynman integrals
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• The Wilson Loop -- Large Spin OPE Dictionary
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond