Global symmetries of Yang-Mills squared in various dimensions

Abstract

Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\le 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each dimension $3\le D\le 10$ we obtain formulae for the algebras $\mathfrak{g}$ and $\mathfrak{h}$ of the U-duality group $G$ and its maximal compact subgroup $H$, respectively, in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.

25 pages, 2 figures, references added, minor typos corrected, further comments on sec. 2.4 included, updated to match version to appear in JHEP

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