Cluster Alphabets from Generalized Worldsheets: A Geometric Approach to Finite Types

Abstract

We provide a systematic derivation of cluster alphabets of finite types. The construction is based on a geometric realization of the generalized worldsheets by gluing and folding a pair of polygons. The cross ratios of the worldsheet z variables are evolved using the Y-system equations. By a new gauge choice, we obtain a simpler set of cluster alphabets than the known ones.

References in corpus (7)

• Bootstrapping the three-loop hexagon
• Motivic Amplitudes and Cluster Coordinates
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Cluster algebras for Feynman integrals
• Cluster adjacency beyond MHV
• Cluster Configuration Spaces of Finite Type
• Notes on Worldsheet-Like Variables for Cluster Configuration Spaces