A note on exemplary off-shell constructions of 4D, $$ \mathcal{N} $$ = 2 supersymmetry representations

Abstract

Abstract We continue the search for rules that govern when off-shell 4D, $$ \mathcal{N} $$ N = ∞ supermultiplets can be combined to form off-shell 4D, $$ \mathcal{N} $$ N = ∈ supermultiplets. We study the 𝕊8 permutations and Height Yielding Matrix Numbers (HYMN) embedded within the adinkras that correspond to these putative off-shell 4D, $$ \mathcal{N} $$ N = 2 supermultiplets. Even though the HYMN definition was designed to distinguish between the raising and lowering of nodes in one dimensional valise supermultiplets, they are shown to accurately select out which combinations of off-shell 4D, $$ \mathcal{N} $$ N = 1 supermultiplets correspond to off-shell 4D, $$ \mathcal{N} $$ N = 2 supermultiplets. Only the combinations of the chiral + vector and chiral + tensor are found to have valises in the same class. This is consistent with the well known structure of 4D, $$ \mathcal{N} $$ N = 2 supermultiplets.