Cluster Alphabets from Generalized Worldsheets: A Geometric Approach to Finite Types
arXiv:2405.04772 · doi:10.1103/PhysRevD.108.105013
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.