Twin Supergravities from Yang-Mills Squared

Abstract: We consider `twin supergravities' - pairs of supergravities with $\mathcal{N}+$ and $\mathcal{N}-$ supersymmetries, $\mathcal{N}+>\mathcal{N}-$, with identical bosonic sectors - in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old. In particular, the matter coupled $\mathcal{N}-$ twins in $D=3,5,6$ and the $\mathcal{N}-=1$ twins in $D=4$ have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories.