Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy

  • Marco Chiodaroli
  • Murat Günaydin
  • Henrik Johansson
  • Radu Roiban
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Scattering Amplitudes Supergravity Models Supersymmetric Gauge Theory 

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Marco Chiodaroli
    • 1
  • Murat Günaydin
    • 2
  • Henrik Johansson
    • 1
    • 3
  • Radu Roiban
    • 2
  1. 1.Department of Physics and AstronomyUppsala UniversityUppsalaSweden
  2. 2.Institute for Gravitation and the CosmosThe Pennsylvania State UniversityUniversity ParkU.S.A.
  3. 3.Nordita, Stockholm University and KTH Royal Institute of TechnologyStockholmSweden

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