Infinite-Dimensional Algebraic $\mathfrak{Spin}$($N$) Structure in Extended/Higher Dimensional SUSY Holoraumy for Valise and On-Shell Supermultiplet Representations

TL;DR

This paper investigates the connection between holoraumy, Hodge duality, and infinite-dimensional algebras in extended supersymmetric theories across various dimensions, revealing dimension-dependent relationships and algebraic structures.

Contribution

It uncovers the dimension-dependent nature of holoraumy and Hodge duality relationships and demonstrates the emergence of an infinite-dimensional algebra extending (N) in reduced one-dimensional theories.

Findings

Holoraumy and Hodge duality are linked in 4D vector-tensor  multiplet.

The relationship between holoraumy and Hodge duality is ephemeral beyond 6D.

Reduction to 1D theories reveals an infinite-dimensional algebra extending (N).

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 $\cal N$ = 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 $\mathfrak{Spin}(N)$.