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 mathcal{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 mathcal{N}=4 supergravity theories. The constructions are illustrated by explicit examples of tree-level and one-loop scattering amplitudes.
Highlights
Einstein’s theory of gravity and spontaneously-broken gauge theory are two of the pillars of our current understanding of the known fundamental interactions of Nature
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
The double-copy construction of a wide class of Yang-Mills-Einstein supergravity (YMESG) theories was given in [27], where it was shown that one of the two gaugetheory factors is a pure SYM theory, and the other is a bosonic YM theory coupled to scalars that transforms in the adjoint representation of both the gauge group and a global symmetry group
Summary
Einstein’s theory of gravity and spontaneously-broken gauge theory are two of the pillars of our current understanding of the known fundamental interactions of Nature. The double-copy construction of a wide class of Yang-Mills-Einstein supergravity (YMESG) theories was given in [27], where it was shown that one of the two gaugetheory factors is a pure SYM theory, and the other is a bosonic YM theory coupled to scalars that transforms in the adjoint representation of both the gauge group and a global symmetry group. The latter theory has trilinear φ3 couplings, and we refer to it as YM + φ3 theory. The scattering amplitudes in a gauge theory with fields in both the adjoint representation and some generic complex representation U of a Lie group can be organized in terms of cubic graphs. At L loops and in D dimensions, such amplitude has the following form
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