Adinkra height yielding matrix numbers: Eigenvalue equivalence classes for minimal four-color adinkras

Abstract

An adinkra is a graph-theoretic representation of space-time supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, = 1 supermultiplets. Valise adinkras, although an important subclass, do not encode all the information present when a 4D supermultiplet is reduced to 1D. Eigenvalue equivalence classes for valise adinkra matrices exist, known as χo equivalence classes, where valise adinkras within the same χo equivalence class are isomorphic in the sense that adinkras within a χo-equivalence class can be transformed into each other via field redefinitions of the nodes. We extend this to non-valise adinkras, via Python code, providing a complete eigenvalue classification of "node-lifting" for all 36,864 valise adinkras associated with the Coxeter group BC4. We term the eigenvalues associated with these node-lifted adinkras Height Yielding Matrix Numbers (HYMNs) and introduce HYMN equivalence classes. These findings have been summarized in a Mathematica notebook that can be found at the HEPTHools Data Repository on GitHub.