Global symmetries of Yang-Mills squared in various dimensions

TL;DR

This paper explores how tensoring super Yang-Mills theories in various dimensions constructs supergravity theories, revealing the structure of their symmetry groups through division algebras and extending to matter couplings.

Contribution

It provides explicit formulas for the U-duality algebras of supergravity theories derived from Yang-Mills tensor products, including matter couplings and non-supersymmetric cases.

Findings

Derived formulas for U-duality algebras in dimensions 3 to 10.

Extended analysis to matter-coupled supergravities.

Connected division algebras with symmetry structures of supergravity.

Abstract

Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\leq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each dimension $3\leq D\leq 10$ 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.