skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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 + φ 3 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.

Authors:
 [1];  [2];  [3];  [2]
  1. Uppsala Univ. (Sweden). Dept. of Physics and Astronomy
  2. Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos
  3. Uppsala Univ. (Sweden). Dept. of Physics and Astronomy; Stockholm Univ. (Sweden); KTH Royal Inst. of Technology, Stockholm (Sweden). Nordita
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States); Uppsala Univ. (Sweden); KTH Royal Inst. of Technology, Stockholm (Sweden)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Knut and Alice Wallenberg Foundation (Sweden); Swedish Research Council (SRC); Ragnar Soderberg Foundation (Sweden)
OSTI Identifier:
1425796
Grant/Contract Number:  
SC0013699; KAW 2013.0235; 621-2014-5722; S1/16
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; scattering amplitudes; supergravity models; supersymmetric gauge theory

Citation Formats

Chiodaroli, Marco, Günaydin, Murat, Johansson, Henrik, and Roiban, Radu. Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy. United States: N. p., 2017. Web. doi:10.1007/JHEP07(2017)002.
Chiodaroli, Marco, Günaydin, Murat, Johansson, Henrik, & Roiban, Radu. Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy. United States. doi:10.1007/JHEP07(2017)002.
Chiodaroli, Marco, Günaydin, Murat, Johansson, Henrik, and Roiban, Radu. Mon . "Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy". United States. doi:10.1007/JHEP07(2017)002. https://www.osti.gov/servlets/purl/1425796.
@article{osti_1425796,
title = {Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy},
author = {Chiodaroli, Marco and Günaydin, Murat and Johansson, Henrik and Roiban, Radu},
abstractNote = {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 + φ 3 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.},
doi = {10.1007/JHEP07(2017)002},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2017,
place = {United States},
year = {2017},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 23 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Pure gravities via color-kinematics duality for fundamental matter
journal, November 2015

  • Johansson, Henrik; Ochirov, Alexander
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)046

Complete N-point superstring disk amplitude II. Amplitude and hypergeometric function structure
journal, August 2013


The double copy: Bremsstrahlung and accelerating black holes
journal, June 2016

  • Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)023

Complete N-point superstring disk amplitude I. Pure spinor computation
journal, August 2013


Coupling Gravitons to Matter
journal, April 2000


New color decompositions for gauge amplitudes at tree and loop level
journal, April 2000


The classical double copy for Taub–NUT spacetime
journal, November 2015


One-loop four-point amplitudes in pure and matter-coupled $ \mathcal{N}\leq 4 $ supergravity
journal, March 2013

  • Carrasco, John Joseph M.; Chiodaroli, Marco; Günaydin, Murat
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)056

Scattering of Massless Particles in Arbitrary Dimensions
journal, October 2014


Compact and non-compact gauged supergravity theories in five dimensions
journal, August 1986


Color/kinematics duality for general abelian orbifolds of $ \mathcal{N} $  = 4 super Yang-Mills theory
journal, January 2014

  • Chiodaroli, M.; Jin, Q.; Roiban, R.
  • Journal of High Energy Physics, Vol. 2014, Issue 1
  • DOI: 10.1007/JHEP01(2014)152

Explicit BCJ numerators from pure spinors
journal, July 2011

  • Mafra, Carlos R.; Schlotterer, Oliver; Stieberger, Stephan
  • Journal of High Energy Physics, Vol. 2011, Issue 7
  • DOI: 10.1007/JHEP07(2011)092

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
journal, March 2012

  • Boels, Rutger H.; Isermann, Reinke Sven
  • Journal of High Energy Physics, Vol. 2012, Issue 3
  • DOI: 10.1007/JHEP03(2012)051

Ambitwistor Strings in Four Dimensions
journal, August 2014


A proof of the explicit minimal-basis expansion of tree amplitudes in gauge field theory
journal, February 2011

  • Chen, Yi-Xin; Du, Yi-Jian; Feng, Bo
  • Journal of High Energy Physics, Vol. 2011, Issue 2
  • DOI: 10.1007/JHEP02(2011)112

Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
journal, July 2015

  • Cachazo, Freddy; He, Song; Yuan, Ellis Ye
  • Journal of High Energy Physics, Vol. 2015, Issue 7
  • DOI: 10.1007/JHEP07(2015)149

Multi-centered N = 2 $$ \mathcal{N}=2 $$ BPS black holes: a double copy description
journal, April 2017

  • Cardoso, G. L.; Nagy, S.; Nampuri, S.
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)037

General matter coupled gauged supergravity in five dimensions
journal, September 2001


New relations for Einstein–Yang–Mills amplitudes
journal, December 2016


New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level
journal, April 2017


Gauging the d = 5 Maxwell/Einstein supergravity theories: More on Jordan algebras
journal, January 1985


Scattering of massless particles: scalars, gluons and gravitons
journal, July 2014

  • Cachazo, Freddy; He, Song; Yuan, Ellis Ye
  • Journal of High Energy Physics, Vol. 2014, Issue 7
  • DOI: 10.1007/JHEP07(2014)033

Monodromy and Jacobi-like relations for color-ordered amplitudes
journal, June 2010

  • Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Søndergaard, Thomas
  • Journal of High Energy Physics, Vol. 2010, Issue 6
  • DOI: 10.1007/JHEP06(2010)003

Relations for Einstein–Yang–Mills amplitudes from the CHY representation
journal, April 2017


N = 8 supergravity
journal, November 1982


Graviton amplitudes from collinear limits of gauge amplitudes
journal, May 2015


Consistency Conditions for Gauge Theory S Matrices from Requirements of Generalized Unitarity
journal, June 2014


New ambitwistor string theories
journal, November 2015

  • Casali, Eduardo; Geyer, Yvonne; Mason, Lionel
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)038

Subleading terms in the collinear limit of Yang–Mills amplitudes
journal, November 2015


Extensions of theories from soft limits
journal, June 2016

  • Cachazo, Freddy; Cha, Peter; Mizera, Sebastian
  • Journal of High Energy Physics, Vol. 2016, Issue 6
  • DOI: 10.1007/JHEP06(2016)170

New Representations of the Perturbative S Matrix
journal, February 2016

  • Baadsgaard, Christian; Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.
  • Physical Review Letters, Vol. 116, Issue 6
  • DOI: 10.1103/PhysRevLett.116.061601

Amplitude relations in non-linear sigma model
journal, January 2014


More on d=5 Maxwell-Einstein supergravity: symmetric spaces and kinks
journal, September 1986


Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010


Perturbative spacetimes from Yang-Mills theory
journal, April 2017

  • Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)069

String-inspired BCJ numerators for one-loop MHV amplitudes
journal, January 2016

  • He, Song; Monteiro, Ricardo; Schlotterer, Oliver
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)171

Einstein-Yang-Mills from pure Yang-Mills amplitudes
journal, October 2016

  • Nandan, Dhritiman; Plefka, Jan; Schlotterer, Oliver
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)070

Complete Construction of Magical, Symmetric, and Homogeneous N = 2 Supergravities as Double Copies of Gauge Theories
journal, June 2016


Black holes and the double copy
journal, December 2014

  • Monteiro, R.; O’Connell, D.; White, C. D.
  • Journal of High Energy Physics, Vol. 2014, Issue 12
  • DOI: 10.1007/JHEP12(2014)056

Higher-spin algebras, holography and flat space
journal, February 2017


The SO(8) supergravity
journal, November 1979


A relation between tree amplitudes of closed and open strings
journal, May 1986


Magic Square from Yang-Mills Squared
journal, April 2014


Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989


Symmetry for Flavor-Kinematics Duality from an Action
journal, March 2017


Higher-Loop Amplitude Monodromy Relations in String and Gauge Theory
journal, November 2016


Amplitude relations in heterotic string theory and Einstein-Yang-Mills
journal, November 2016


On four-point interactions in massless higher spin theory in flat space
journal, April 2017


A magic pyramid of supergravities
journal, April 2014

  • Anastasiou, A.; Borsten, L.; Duff, M. J.
  • Journal of High Energy Physics, Vol. 2014, Issue 4
  • DOI: 10.1007/JHEP04(2014)178

Minimal Basis for Gauge Theory Amplitudes
journal, October 2009


Closed string amplitudes as single-valued open string amplitudes
journal, April 2014


Graviton as a pair of collinear gauge bosons
journal, December 2014


Einstein-Yang-Mills scattering amplitudes from scattering equations
journal, January 2015

  • Cachazo, Freddy; He, Song; Yuan, Ellis Ye
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)121

Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
journal, October 2015

  • Mafra, Carlos R.; Schlotterer, Oliver
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)124

Towards one-loop SYM amplitudes from the pure spinor BRST cohomology: Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
journal, January 2015


Berends-Giele recursions and the BCJ duality in superspace and components
journal, March 2016

  • Mafra, Carlos R.; Schlotterer, Oliver
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)097

Color decomposition of one-loop amplitudes in gauge theories
journal, September 1991


The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras
journal, August 1984


Scattering amplitudes in N = 2 $$ \mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity
journal, January 2015

  • Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik
  • Journal of High Energy Physics, Vol. 2015, Issue 1
  • DOI: 10.1007/JHEP01(2015)081

Non-linear gauge transformations in D = 10 SYM theory and the BCJ duality
journal, March 2016

  • Lee, Seungjin; Mafra, Carlos R.; Schlotterer, Oliver
  • Journal of High Energy Physics, Vol. 2016, Issue 3
  • DOI: 10.1007/JHEP03(2016)090

Yang-Mills Origin of Gravitational Symmetries
journal, December 2014


Global symmetries of Yang-Mills squared in various dimensions
journal, January 2016

  • Anastasiou, A.; Borsten, L.; Hughes, M. J.
  • Journal of High Energy Physics, Vol. 2016, Issue 1
  • DOI: 10.1007/JHEP01(2016)148

A double copy for N = 2 $$ \mathcal{N}=2 $$ supergravity: a linearised tale told on-shell
journal, October 2016

  • Cardoso, G. L.; Nagy, S.; Nampuri, S.
  • Journal of High Energy Physics, Vol. 2016, Issue 10
  • DOI: 10.1007/JHEP10(2016)127

Gauged N = 8 supergravity in five dimensions
journal, May 1985


Ambitwistor strings and the scattering equations
journal, July 2014


Polylogarithms, multiple zeta values and superstring amplitudes
journal, August 2013

  • Broedel, J.; Schlotterer, O.; Stieberger, S.
  • Fortschritte der Physik, Vol. 61, Issue 9
  • DOI: 10.1002/prop.201300019

    Works referencing / citing this record:

    String Amplitudes from Field-Theory Amplitudes and Vice Versa
    journal, May 2019