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 ones. 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 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.

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein–Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu–Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard–Zumino duality on the world-sheet. An equivalent polynomial ‘Polyakov-type’ action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear.

We consider a deformation of the well-known stu model of N = 2, D = 4 supergravity, characterized by a non-homogeneous special Kähler manifold, and by the smallest electric-magnetic duality Lie algebra consistent with its upliftability to five dimensions. We explicitly solve the BPS attractor equations and construct static supersymmetric black holes with radial symmetry, in the context of U(1) dyonic Fayet-Iliopoulos gauging, focussing on axion-free solutions. Due to non-homogeneity of the scalar manifold, the model evades the analysis recently given in the literature. The relevant physical properties of the resulting black hole solution are discussed.

Six-dimensional spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, $SU\left(5\right)$, and $Spin\left(10\right)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $Ad{S}_5\to d{S}_4$, or simply broken to $Spin(3,1)$ of a Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $Ad{S}_3$ with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor $\mathbf{128}$ of $Spin(4,12)$ is found with $Spin\left(3\right)$ flavor symmetry inside $E_{8(-24)}$. The 128 of $Spin(12,4)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(12,4)=\left(\mathbb{O}sx\mathbb{O}\right){\mathbb{P}}^2$.

Supersymmetric theories with the same bosonic content but different fermions, aka twins, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $$ \mathcal{N} $$ N = 3 and $$ \mathcal{N} $$ N = 1 theories in D = 4 space-time dimensions, can also be twin. We provide evidence from three different perspectives: (i) a twin S-fold construction, (ii) a double-copy argument and (iii) by identifying candidate twin holographically dual gauged supergravity theories. Furthermore, twin W-supergravity theories then follow by applying the double-copy prescription to exotic super conformal field theories.