Infinite-dimensional algebraic $$ \mathfrak{Spin} $$(N) structure in extended/higher dimensional SUSY holoraumy for valise and on shell supermultiplet representations

Abstract

Abstract We explore the relationship between holoraumy and Hodge duality beyond four dimensions. We find this relationship to be ephemeral beyond six dimensions: it is not demanded by the structure of such supersymmetrical theories. In four dimensions for the case of the vector-tensor $$ \mathcal{N} $$ N = 4 multiplet, however, we show that such a linkage is present. Reduction to 1D theories presents evidence for a linkage from higher-dimensional supersymmetry to an infinite-dimensional algebra extending $$ \mathfrak{Spin} $$ Spin (N).