We consider twin supergravities-pairs of supergravities with N+ and N- supersymmetries, N+ > 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 YangMills factors. This procedure generates newtheories from old ones. In particular, the matter coupled N(-)twins in D = 3, 5, 6 and the N- = 1 twins inD = 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 bifundamental scalar that couples to the well-known biadjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorization into left and right super Yang-Mills-matter theories.
Using simple symmetry arguments we classify the ungauged D = 4, N = 2 supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of N = 2 and N= 0 matter-coupled Yang-Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the T-3 model.
The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity-two-form-dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation. The inclusion of ghost fields facilitates the separation of the graviton and dilaton. The gravitational gauge fixing term is uniquely determined by those of the Yang-Mills factors which can be freely chosen. Moreover, the resulting gravity-two-form-dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anticommute as a direct consequence of the formalism.