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

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 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 Spin(N).

Automated summary

In this article, we explore the relationship between holoraumy and Hodge duality, and find that this relationship only holds in four dimensions for a specific case. Beyond six dimensions, this relationship is not supported by the structure of supersymmetric theories. Moreover, we provide evidence for a linkage from higher-dimensional supersymmetry to an infinite-dimensional algebra extending Spin(N) through the reduction to 1D theories.