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

Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu

doi:10.1007/JHEP07(2017)002

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:

Chiodaroli, Marco ^[1]; Günaydin, Murat ^[2]; Johansson, Henrik ^[3]; Roiban, Radu ^[2]

Uppsala Univ. (Sweden). Dept. of Physics and Astronomy
Pennsylvania State Univ., University Park, PA (United States). Inst. for Gravitation and the Cosmos
Uppsala Univ. (Sweden). Dept. of Physics and Astronomy; Stockholm Univ. (Sweden); KTH Royal Inst. of Technology, Stockholm (Sweden). Nordita

Publication Date:: Mon Jul 03 00:00:00 EDT 2017

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); 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.

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                    Chiodaroli, Marco, Günaydin, Murat, Johansson, Henrik, & Roiban, Radu. Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy.  United States.  https://doi.org/10.1007/JHEP07(2017)002

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                    Chiodaroli, Marco, Günaydin, Murat, Johansson, Henrik, and Roiban, Radu. Mon .  
"Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy".  United States.  https://doi.org/10.1007/JHEP07(2017)002.  https://www.osti.gov/servlets/purl/1425796.

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@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         = {Mon Jul 03 00:00:00 EDT 2017},

  month        = {Mon Jul 03 00:00:00 EDT 2017}

}

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text, January 2018

Faller, Josua; Plefka, Jan
arXiv
DOI: 10.48550/arxiv.1812.04053

Supersymmetry constraints on U-duality invariant deformations of $N \geq 5$ Supergravity
text, January 2018

Gunaydin, Murat; Kallosh, Renata
arXiv
DOI: 10.48550/arxiv.1812.08758

Expansion of Einstein-Yang-Mills theory by Differential Operators
text, January 2019

Feng, Bo; Li, Xiaodi; Zhou, Kang
arXiv
DOI: 10.48550/arxiv.1904.05997

Monodromy relations from twisted homology
text, January 2019

Casali, Eduardo; Mizera, Sebastian; Tourkine, Piotr
arXiv
DOI: 10.48550/arxiv.1910.08514

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Similar Records

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

Abstract

Citation Formats

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

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

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

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

Explicit BCJ numerators from pure spinors journal, July 2011

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

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

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

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

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

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

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

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

Extensions of theories from soft limits journal, June 2016

New Representations of the Perturbative S Matrix journal, February 2016

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

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

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

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

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

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

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

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

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

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

Yang-Mills Origin of Gravitational Symmetries journal, December 2014

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

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

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

Minimal Basis for Gauge Theory Amplitudes text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes text, January 2010

A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory text, January 2011

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts text, January 2011

Polylogarithms, Multiple Zeta Values and Superstring Amplitudes text, January 2013

Amplitude Relations in Non-linear Sigma Model text, January 2013

Ambitwistor strings and the scattering equations text, January 2013

Closed String Amplitudes as Single-Valued Open String Amplitudes text, January 2014

Pure Gravities via Color-Kinematics Duality for Fundamental Matter text, January 2014

Graviton Amplitudes from Collinear Limits of Gauge Amplitudes text, January 2015

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

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

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

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

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

Explicit BCJ numerators from pure spinors
journal, July 2011

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

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

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

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

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

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

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

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

Extensions of theories from soft limits
journal, June 2016

New Representations of the Perturbative $S$ Matrix
journal, February 2016

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

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

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

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

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

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

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

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

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

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

Yang-Mills Origin of Gravitational Symmetries
journal, December 2014

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

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

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

Minimal Basis for Gauge Theory Amplitudes
text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
text, January 2010

A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory
text, January 2011

Yang-Mills amplitude relations at loop level from non-adjacent BCFW shifts
text, January 2011

Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
text, January 2013

Amplitude Relations in Non-linear Sigma Model
text, January 2013

Ambitwistor strings and the scattering equations
text, January 2013

Closed String Amplitudes as Single-Valued Open String Amplitudes
text, January 2014

Pure Gravities via Color-Kinematics Duality for Fundamental Matter
text, January 2014

Graviton Amplitudes from Collinear Limits of Gauge Amplitudes
text, January 2015

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

The classical double copy for Taub-NUT spacetime
text, January 2015

String-inspired BCJ numerators for one-loop MHV amplitudes
text, January 2015

Berends-Giele recursions and the BCJ duality in superspace and components
text, January 2015