Adinkra Height Yielding Matrix Numbers: Eigenvalue Equivalence Classes for Minimal Four-Color Adinkras

Abstract

An adinkra is a graph-theoretic representation of spacetime supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, $\mathcal{N}$ = 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 ${\chi }_{\mathrm{o}}$ equivalence classes, where valise adinkras within the same ${\chi }_{\mathrm{o}}$ equivalence class are isomorphic in the sense that adinkras within a ${\chi }_{\mathrm{o}}$-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 $BC{}_4$. 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 found at the HEPTHools Data Repository (https://hepthools.github.io/Data/) on GitHub.

Added references, made small text changes, 39 pages, 5 figures

References in corpus (8)

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• Spin Holography via Dimensional Enhancement
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Cited by in corpus (4)

• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• The 300 "Correlators" Suggests 4D, $\mathcal{N}$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras
• Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces