A note on exemplary off-shell constructions of 4D, $$ \mathcal{N} $$ = 2 supersymmetry representations
Devin Bristow (Natural Science Division, Pepperdine University, 24255 Pacific Coast Highway, Malibu, CA, 90263, USA); John Caporaletti (Department of Physics, University of Maryland, 4150 Campus Dr, College Park, MD, 20742-4111, USA); Aleksander Cianciara (Department of Physics, Brown University, 182 Hope Street, Providence, RI, 02912, USA, Brown Center for Theoretical Physics, 340 Brook Street, Providence, RI, 02912, USA); S. Gates (Department of Physics, Brown University, 182 Hope Street, Providence, RI, 02912, USA, Brown Center for Theoretical Physics, 340 Brook Street, Providence, RI, 02912, USA); Delina Levine (Department of Physics, University of Maryland, 4150 Campus Dr, College Park, MD, 20742-4111, USA); et al - Show all 6 authors
We continue the search for rules that govern when off-shell 4D, $$ \mathcal{N} $$ = ∞ supermultiplets can be combined to form off-shell 4D, $$ \mathcal{N} $$ = ∈ supermultiplets. We study the 𝕊8 permutations and Height Yielding Matrix Numbers (HYMN) embedded within the adinkras that correspond to these putative off-shell 4D, $$ \mathcal{N} $$ = 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, $$ \mathcal{N} $$ = 1 supermultiplets correspond to off-shell 4D, $$ \mathcal{N} $$ = 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, $$ \mathcal{N} $$ = 2 supermultiplets.
