Symbol Alphabets from Plabic Graphs II: Rational Letters

Abstract

Symbol alphabets of n-particle amplitudes in N=4 super-Yang-Mills theory are known to contain certain cluster variables of Gr(4,n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n=8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of Gr_+(n-4,n).

arXiv comment10 pages, 2 figures; v2: minor typos corrected

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Cited by in corpus (14)

• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Antipodal Self-Duality for a Four-Particle Form Factor
• Notes on cluster algebras and some all-loop Feynman integrals
• Truncated cluster algebras and Feynman integrals with algebraic letters
• Symbol Alphabets from Tensor Diagrams
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Schubert Problems, Positivity and Symbol Letters
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• The recursive structure of Baikov representations I: generics and application to symbology
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras