Abstract

Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons. These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + ϕ3 theory. The construction outlined in this paper holds in general dimension and extends straightforwardly to supergravity theories. For one, two, and three external gravitons, our expressions give identical or simpler presentations of amplitudes already constructed through string-theory considerations or the scattering equations formalism. Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons. We also present explicit expressions for all-loop single-graviton Einstein-Yang-Mills amplitudes in terms of Yang-Mills amplitudes and, through gauge invariance, derive new all-loop amplitude relations for Yang-Mills theory.

Highlights

  • Using the double-copy construction of Yang-Mills-Einstein theories formulated in our earlier work, we obtain compact presentations for single-trace Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an arbitrary number of gluons

  • These are written as linear combinations of color-ordered Yang-Mills trees, where the coefficients are given by color/kinematics-satisfying numerators in a Yang-Mills + φ3 theory

  • Our results are based on color/kinematics duality and gauge invariance, and strongly hint at a recursive structure underlying the single-trace amplitudes with an arbitrary number of gravitons

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Summary

Double-copy construction for YME amplitudes

We first argue that the double copy of scattering amplitudes of two gauge theories that obey color/kinematics duality always leads to the scattering amplitudes of some theory of gravity (i.e. invariant under diffeomorphisms). Note that the ideas presented here have been partially addressed in various contexts within the double-copy literature [1, 2, 4, 43, 60]; here we give a more complete argument We conclude the section by reviewing the construction of the amplitudes of certain classes of YME (super)gravity theories. L-loop n-point scattering amplitudes in any matter-coupled gauge theory can be organized as

Si cini Di
Explicit YME amplitudes
YME amplitudes
Towards six gravitons and beyond
Loop-level amplitudes
Other theories
Discussion and outlook
A Novel presentation of the BCJ relations
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