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, [Formula: see text] 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 [Formula: see text] equivalence classes, where valise adinkras within the same [Formula: see text] equivalence class are isomorphic in the sense that adinkras within a [Formula: see text]-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 [Formula: see text]. 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.