Abstract
Tensoring two on-shell super Yang-Mills multiplets in dimensions D ≤ 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 ≤ D ≤ 10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H 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.
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Anastasiou, A., Borsten, L., Hughes, M.J. et al. Global symmetries of Yang-Mills squared in various dimensions. J. High Energ. Phys. 2016, 148 (2016). https://doi.org/10.1007/JHEP01(2016)148
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DOI: https://doi.org/10.1007/JHEP01(2016)148