Spontaneously Broken Yang-Mills-Einstein Supergravities as Double Copies

TL;DR

This work extends color/kinematics duality and the double-copy construction to spontaneously-broken Yang-Mills-Einstein supergravity theories, focusing on adjoint-Higgs (Coulomb-branch) dynamics and explicit global-symmetry breaking. It presents a general framework where one gauge copy is a spontaneously-broken YM (or YM with SUSY) and the other is a bosonic YM+φ^3 theory with explicit global breaking, with extended kinematic identities ensuring a valid gravity double copy. The authors apply the construction to ${\cal N}=2$ YMESG theories in the generic Jordan family in four and five dimensions, map supergravity fields to double-copy constituents, and demonstrate tree-level and one-loop amplitudes; they also outline consistent extensions to ${\cal N}=4$ and discuss the Coulomb-branch interpretation as a higher-dimensional origin. Overall, the paper provides concrete amplitude-based evidence for a robust double-copy structure on the Coulomb branch and offers a detailed field-map between broken gauge theories and their gravitational avatars, opening avenues for broader class constructions and loop-level analyses.

Abstract

Color/kinematics duality and the double-copy construction have proved to be systematic tools for gaining new insight into gravitational theories. Extending our earlier work, in this paper we introduce new double-copy constructions for large classes of spontaneously-broken Yang-Mills-Einstein theories with adjoint Higgs fields. One gauge-theory copy entering the construction is a spontaneously-broken (super-)Yang-Mills theory, while the other copy is a bosonic Yang-Mills-scalar theory with trilinear scalar interactions that display an explicitly-broken global symmetry. We show that the kinematic numerators of these gauge theories can be made to obey color/kinematics duality by exhibiting particular additional Lie-algebraic relations. We discuss in detail explicit examples with N=2 supersymmetry, focusing on Yang-Mills-Einstein supergravity theories belonging to the generic Jordan family in four and five dimensions, and identify the map between the supergravity and double-copy fields and parameters. We also briefly discuss the application of our results to N=4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.

Figures (7)

• Figure 1: The two cubic types of interactions for fields in adjoint representation and a generic complex representation. We organize the amplitudes around cubic graphs with these two types of vertices, and the corresponding color factors are contractions of the structure constants and the generators.
• Figure 2: Pictorial form of the basic color and kinematic Lie-algebraic relations: (a) the Jacobi relations for fields in the adjoint representation, and (b) the commutation relation for fields in a generic complex representation.
• Figure 3: Additional types of cubic interactions that are obtained after the gauge symmetry is spontaneously-broken in a purely adjoint theory. The resulting amplitudes are organized around cubic graphs where these vertices are included. The corresponding color factors are contractions of the various types of structure constants.
• Figure 4: Pictorial representation of additional color Lie-algebra relations that are obtained after the gauge symmetry spontaneously-broken in a purely adjoint theory. These are also pictorial representations of the kinematic algebra that should be imposed on diagram numerators in the context of color/kinematics duality. The relations are generalizations of the Jacobi identity. Curly lines represent unbroken adjoint states (massless fields) and double lines represent broken non-hermitian states (massive fields). Solid fat lines in (d) represent sums over all three types of states (the massless and two conjugates of the massive ones), giving seven terms in the (d) identity.
• Figure 5: Seven separate contributions to tree amplitudes with four massive scalars. Dashed lines with arrows denote complex (massive) scalars. In diagram (1) and (4) the exchanged particle is a sum of a massless scalar and a gluon.