Twin supergravities from Yang-Mills theory squared

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.

Figure 1

Tree-level Feynman diagrams for the four-point gluon-gluon-quark-antiquark interaction.

Figure 2

Double-line tree-level Feynman diagrams for the four-point (bi-adj.)-(bi-adj.)-(bi-fund.)-(bi-fund.) interaction for the scalar theory in Eq. (25). The curly (straight) double lines represent the biadjoint (bifundamental) representation of the global $G\times \tilde{G}$ symmetry. Each diagram is the double-copy of the corresponding gluon-quark diagram shorn of its kinematic data.

Figure 3

Tree-level Feynman diagrams for the five-point quark-antiquark-quark’-antiquark’-gluon interaction.

Figure 4

Double-line tree-level Feynman diagrams for the five-point (bi-fund.)-(bi-fund.)-(bi-fund’.)-(bi-fund’.)-(bi-adj.) interaction for the scalar theory in Eq. (b3). The curly (straight) double lines represent the biadjoint (bifundamental) representation of the global $G\times \tilde{G}$ symmetry. Each diagram is the double-copy of the corresponding gluon-quark diagram shawn of its kinematic data.