Symbol Alphabets from Plabic Graphs

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. In this paper we suggest an algorithm for computing these symbol alphabets from plabic graphs by solving matrix equations of the form C Z = 0 to associate functions on Gr(m,n) to parameterizations of certain cells of Gr(k,n) indexed by plabic graphs. For m=4 and n=8 we show that this association precisely reproduces the 18 algebraic symbol letters of the two-loop NMHV eight-point amplitude from four plabic graphs.

arXiv comment19 pages; v2: minor corrections and improvements

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Cited by in corpus (23)

• Cluster algebras for Feynman integrals
• Landau Discriminants
• 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
• The symbol and alphabet of two-loop NMHV amplitudes from $\bar{Q}$ equations
• 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
• A Note on Letters of Yangian Invariants
• Intersection theory rules symbology
• The Two-Loop Remainder Function for Eight and Nine Particles
• Symbol Alphabets from Plabic Graphs II: Rational Letters
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Comments on all-loop constraints for scattering amplitudes and Feynman integrals
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Non-planar BCFW Grassmannian Geometries
• Bootstrapping octagons in reduced kinematics from $A_2$ cluster algebras
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills
• Plabic Tangles and Cluster Promotion Maps