Cluster Polylogarithms for Scattering Amplitudes

Abstract

Motivated by the cluster structure of two-loop scattering amplitudes in N=4 Yang-Mills theory we define "cluster polylogarithm functions". We find that all such functions of weight 4 are made up of a single simple building block associated to the A_2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A_2 building blocks arrange themselves to form a unique function associated to the A_3 cluster algebra. This A_3 function manifests all of the cluster algebraic structure of the two-loop n-particle MHV amplitudes for all n, and we use it to provide an explicit representation for the most complicated part of the n=7 amplitude as an example.

22 pages, 8 figures; v2: minor corrections and clarifications

References in corpus (5)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Analytic Results for MHV Wilson Loops
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• Multiple zeta values and periods of moduli spaces ${\mathfrak{M}}_{0,n}$
• Collinear and Regge behavior of 2 -> 4 MHV amplitude in N = 4 super Yang-Mills theory

Cited by in corpus (14)

• Lectures on differential equations for Feynman integrals
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• The last of the simple remainders
• Fermionic pentagons and NMHV hexagon
• Analytic structure of the $n=7$ scattering amplitude in $\mathcal{N}=4$ SYM theory at multi-Regge kinematics: Conformal Regge pole contribution
• On factorization of multiparticle pentagons
• Cluster Algebras and the Positive Grassmannian
• Non-Planar On-Shell Diagrams
• Anatomy of the Amplituhedron
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• A walk on sunset boulevard
• The long road from Regge poles to the LHC