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Twin Supergravities from Yang-Mills Squared

A. Anastasiou, L. Borsten, M. J. Duff, M. J. Hughes, A. Marrani, S. Nagy, M. Zoccali

TL;DR

This paper shows that twin supergravities with identical bosonic sectors emerge systematically from a Yang-Mills squared construction, where left and right super-Yang-Mills multiplets are tensored and then truncated to yield complementary pairs $(\mathcal{N}_+, \mathcal{N}_-)$. The authors formalise a general double-copy procedure, introduce a bi-adjoint/bifundamental spectator scalar to preserve symmetry mappings, and demonstrate how matter couplings produce new twins not previously obtained in double-copy approaches, notably in $D=3,4,5,6$. They exemplify the construction with a detailed $D=4$, $(6,2)$ twin and provide a comprehensive account of the pyramid and triplet structures across dimensions, including isolated twins outside the pyramid and multiple factorisations. The work clarifies when oxidation preserves twinness and highlights the role of representation content and chirality in determining possible factorisations, while pointing toward a broader classification of all alternative factorisations and double-copy-constructible theories. Overall, the results expand the landscape of gravity theories accessible via the Yang-Mills double-copy, with implications for amplitudes, symmetry realization, and spectral organization of supergravity theories.

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.

Twin Supergravities from Yang-Mills Squared

TL;DR

This paper shows that twin supergravities with identical bosonic sectors emerge systematically from a Yang-Mills squared construction, where left and right super-Yang-Mills multiplets are tensored and then truncated to yield complementary pairs . The authors formalise a general double-copy procedure, introduce a bi-adjoint/bifundamental spectator scalar to preserve symmetry mappings, and demonstrate how matter couplings produce new twins not previously obtained in double-copy approaches, notably in . They exemplify the construction with a detailed , twin and provide a comprehensive account of the pyramid and triplet structures across dimensions, including isolated twins outside the pyramid and multiple factorisations. The work clarifies when oxidation preserves twinness and highlights the role of representation content and chirality in determining possible factorisations, while pointing toward a broader classification of all alternative factorisations and double-copy-constructible theories. Overall, the results expand the landscape of gravity theories accessible via the Yang-Mills double-copy, with implications for amplitudes, symmetry realization, and spectral organization of supergravity theories.

Abstract

We consider `twin supergravities' - pairs of supergravities with and supersymmetries, , 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 twins in and the twins in 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.

Paper Structure

This paper contains 10 sections, 78 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Twin supergravity theories
  3. Twins from super Yang-Mills squared
  4. Example: the $D=4, (6,2)$ twin theories
  5. Summary: the pyramid twins in $D=3, 4, 5, 6$
  6. The triplets
  7. Other twins
  8. Conclusions
  9. Irreducible Riemannian globally symmetric Kähler and Quaternionic Manifolds
  10. Bi-adjoint coupled to bi-fundamental scalar theory: a 5-point example

Figures (4)

  • Figure 1: Tree-level Feynman diagrams for the 4-point gluon-gluon-quark-antiquark interaction.
  • Figure 2: Double-line tree-level Feynman diagrams for the 4-point (bi-adj.)-(bi-adj.)-(bi-fund.)-(bi-fund.) interaction for the scalar theory in \ref{['bifundscalar']}. The curly (straight) double-lines represent the bi-adjoint (bi-fundamental) 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.
  • Figure 3: Tree-level Feynman diagrams for the 5-point quark-antiquark-quark'-antiquark'-gluon interaction.
  • Figure 4: Double-line tree-level Feynman diagrams for the 5-point (bi-fund.)-(bi-fund.)-(bi-fund'.)-(bi-fund'.)-(bi-adj.) interaction for the scalar theory in \ref{['bifundscalar_flavour']}. The curly (straight) double-lines represent the bi-adjoint (bi-fundamental) 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.