Topological Characterization of Adinkra Heights

Abstract

Adinkras are highly structured bipartite graphs that encapsulate 1D supersymmetry representations. We classify hypercube Adinkra heights with one, two, three or four edge colors using a graph-theoretic notion of equivalence. For the 990 distinct height functions in the case of four edge colors, we show that these classes match modified twisted character classes bijectively and provide a finer classification than spectral Height Yielding Matrix Numbers (HYMNs). We also relate our classification to the physics of the two-dimensional chiral and twisted chiral supermultiplets.