Covariant color-kinematics duality

Cheung, Clifford; Mangan, James

doi:10.1007/jhep11(2021)069

Covariant color-kinematics duality

Journal Article · Wed Nov 10 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep11(2021)069· OSTI ID:1976578

Cheung, Clifford ^[1]; ^[2]

California Institute of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States)

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/$$\square$$ is replaced with covariant 1/D². Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F³ theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F³ theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Walter Burke Institute

Grant/Contract Number:: SC0011632

OSTI ID:: 1976578

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 11 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

References (73)

The momentum kernel of gauge and gravity theories Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Søndergaard, Thomas Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)001	journal	January 2011
All tree-level amplitudes in massless QCD Dixon, Lance J.; Henn, Johannes M.; Plefka, Jan Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)035	journal	January 2011
Scattering amplitudes in N = 2 $$ \mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)081	journal	January 2015
String-inspired BCJ numerators for one-loop MHV amplitudes He, Song; Monteiro, Ricardo; Schlotterer, Oliver Journal of High Energy Physics, Vol. 2016, Issue 1 https://doi.org/10.1007/JHEP01(2016)171	journal	January 2016
Twofold symmetries of the pure gravity action Cheung, Clifford; Remmen, Grant N. Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)104	journal	January 2017
A periodic table of effective field theories Cheung, Clifford; Kampf, Karol; Novotny, Jiri Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/JHEP02(2017)020	journal	February 2017
Unifying relations for scattering amplitudes Cheung, Clifford; Shen, Chia-Hsien; Wen, Congkao Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)095	journal	February 2018
The classical double copy of a point charge Kim, Kwangeon; Lee, Kanghoon; Monteiro, Ricardo Journal of High Energy Physics, Vol. 2020, Issue 2 https://doi.org/10.1007/JHEP02(2020)046	journal	February 2020
Color/kinematics duality in AdS4 Armstrong, Connor; Lipstein, Arthur E.; Mei, Jiajie Journal of High Energy Physics, Vol. 2021, Issue 2 https://doi.org/10.1007/JHEP02(2021)194	journal	February 2021
An algebraic approach to BCJ numerators Fu, Chih-Hao; Du, Yi-Jian; Feng, Bo Journal of High Energy Physics, Vol. 2013, Issue 3 https://doi.org/10.1007/JHEP03(2013)050	journal	March 2013
The kinematic algebras from the scattering equations Monteiro, Ricardo; O’Connell, Donal Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)110	journal	March 2014
Berends-Giele recursions and the BCJ duality in superspace and components Mafra, Carlos R.; Schlotterer, Oliver Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)097	journal	March 2016
BCJ numerators from reduced Pfaffian Du, Yi-Jian; Teng, Fei Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)033	journal	April 2017
Pions as gluons in higher dimensions Cheung, Clifford; Remmen, Grant N.; Shen, Chia-Hsien Journal of High Energy Physics, Vol. 2018, Issue 4 https://doi.org/10.1007/JHEP04(2018)129	journal	April 2018
Tree-level amplitudes in the nonlinear sigma model Kampf, Karol; Novotný, Jirí; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)032	journal	May 2013
Classical solutions and their double copy in split signature Monteiro, Ricardo; O’Connell, Donal; Veiga, David Peinador Journal of High Energy Physics, Vol. 2021, Issue 5 https://doi.org/10.1007/JHEP05(2021)268	journal	May 2021
Algebras for amplitudes Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Monteiro, Ricardo Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)061	journal	June 2012
The double copy: Bremsstrahlung and accelerating black holes Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)023	journal	June 2016
Inverse of the string theory KLT kernel Mizera, Sebastian Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/JHEP06(2017)084	journal	June 2017
The kinematic algebra from the self-dual sector Monteiro, Ricardo; O’Connell, Donal Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)007	journal	July 2011
Explicit BCJ numerators from pure spinors Mafra, Carlos R.; Schlotterer, Oliver; Stieberger, Stephan Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)092	journal	July 2011
Scattering of massless particles: scalars, gluons and gravitons Cachazo, Freddy; He, Song; Yuan, Ellis Ye Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)033	journal	July 2014
Scattering equations and virtuous kinematic numerators and dual-trace functions Naculich, Stephen G. Journal of High Energy Physics, Vol. 2014, Issue 7 https://doi.org/10.1007/JHEP07(2014)143	journal	July 2014
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM Cachazo, Freddy; He, Song; Yuan, Ellis Ye Journal of High Energy Physics, Vol. 2015, Issue 7 https://doi.org/10.1007/JHEP07(2015)149	journal	July 2015
Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)002	journal	July 2017
A new gauge-invariant double copy for heavy-mass effective theory Brandhuber, Andreas; Chen, Gang; Travaglini, Gabriele Journal of High Energy Physics, Vol. 2021, Issue 7 https://doi.org/10.1007/JHEP07(2021)047	journal	July 2021
On the conformal symmetry of exceptional scalar theories Farnsworth, Kara; Hinterbichler, Kurt; Hulík, Ondřej Journal of High Energy Physics, Vol. 2021, Issue 7 https://doi.org/10.1007/JHEP07(2021)198	journal	July 2021
Note on symmetric BCJ numerator Fu, Chih-Hao; Du, Yi-Jian; Feng, Bo Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)098	journal	August 2014
Kinematic numerators from the worldsheet: cubic trees from labelled trees He, Song; Hou, Linghui; Tian, Jintian Journal of High Energy Physics, Vol. 2021, Issue 8 https://doi.org/10.1007/JHEP08(2021)118	journal	August 2021
Manifesting color-kinematics duality in the scattering equation formalism Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H. Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)094	journal	September 2016
Explicit BCJ numerators of nonlinear simga model Du, Yi-Jian; Fu, Chih-Hao Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)174	journal	September 2016
Hidden simplicity of the gravity action Cheung, Clifford; Remmen, Grant N. Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)002	journal	September 2017
Expansion of Einstein-Yang-Mills amplitude Fu, Chih-Hao; Du, Yi-Jian; Huang, Rijun Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)021	journal	September 2017
A vertex operator algebra construction of the colour-kinematics dual numerator Fu, Chih-Hao; Vanhove, Pierre; Wang, Yihong Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)141	journal	September 2018
Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators Broedel, Johannes; Dixon, Lance J. Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)091	journal	October 2012
BCJ relations from a new symmetry of gauge-theory amplitudes Brown, Robert W.; Naculich, Stephen G. Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)130	journal	October 2016
Perturbiner methods for effective field theories and the double copy Mizera, Sebastian; Skrzypek, Barbara Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)018	journal	October 2018
Algorithmic construction of SYM multiparticle superfields in the BCJ gauge Bridges, Elliot; Mafra, Carlos R. Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)022	journal	October 2019
Next-to-MHV Yang-Mills kinematic algebra Chen, Gang; Johansson, Henrik; Teng, Fei Journal of High Energy Physics, Vol. 2021, Issue 10 https://doi.org/10.1007/JHEP10(2021)042	journal	October 2021
BCJ amplitude relations for Anti-de Sitter boundary correlators in embedding space Diwakar, Pranav; Herderschee, Aidan; Roiban, Radu Journal of High Energy Physics, Vol. 2021, Issue 10 https://doi.org/10.1007/JHEP10(2021)141	journal	October 2021
On the kinematic algebra for BCJ numerators beyond the MHV sector Chen, Gang; Johansson, Henrik; Teng, Fei Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/JHEP11(2019)055	journal	November 2019
Scattering equations in AdS: scalar correlators in arbitrary dimensions Eberhardt, Lorenz; Komatsu, Shota; Mizera, Sebastian Journal of High Energy Physics, Vol. 2020, Issue 11 https://doi.org/10.1007/JHEP11(2020)158	journal	November 2020
Black holes and the double copy Monteiro, R.; O’Connell, D.; White, C. D. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)056	journal	December 2014
Efficient calculation of crossing symmetric BCJ tree numerators Edison, Alex; Teng, Fei Journal of High Energy Physics, Vol. 2020, Issue 12 https://doi.org/10.1007/JHEP12(2020)138	journal	December 2020
Multi-parton amplitudes in gauge theories Mangano, Michelangelo L.; Parke, Stephen J. Physics Reports, Vol. 200, Issue 6 https://doi.org/10.1016/0370-1573(91)90091-Y	journal	February 1991
Antisymmetric tensor gauge theories and non-linear σ-models Freedman, Daniel Z.; Townsend, P. K. Nuclear Physics B, Vol. 177, Issue 2 https://doi.org/10.1016/0550-3213(81)90392-8	journal	January 1981
A relation between tree amplitudes of closed and open strings Kawai, H.; Lewellen, D. C.; Tye, S. -H. H. Nuclear Physics B, Vol. 269, Issue 1 https://doi.org/10.1016/0550-3213(86)90362-7	journal	May 1986
Recursive calculations for processes with n gluons Berends, F. A.; Giele, W. T. Nuclear Physics B, Vol. 306, Issue 4 https://doi.org/10.1016/0550-3213(88)90442-7	journal	September 1988
New color decompositions for gauge amplitudes at tree and loop level Del Duca, Vittorio; Dixon, Lance; Maltoni, Fabio Nuclear Physics B, Vol. 571, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00809-3	journal	April 2000
Analytic representations of Yang–Mills amplitudes Bjerrum-Bohr, N. E. J.; Bourjaily, Jacob L.; Damgaard, Poul H. Nuclear Physics B, Vol. 913 https://doi.org/10.1016/j.nuclphysb.2016.10.012	journal	December 2016
The classical double copy for Taub–NUT spacetime Luna, Andrés; Monteiro, Ricardo; O'Connell, Donal Physics Letters B, Vol. 750 https://doi.org/10.1016/j.physletb.2015.09.021	journal	November 2015
On tree amplitudes in gauge theory and gravity Arkani-Hamed, Nima; Kaplan, Jared Journal of High Energy Physics, Vol. 2008, Issue 04 https://doi.org/10.1088/1126-6708/2008/04/076	journal	April 2008
All tree-level amplitudes in 𝒩 = 4 SYM Drummond, J. M.; Henn, J. M. Journal of High Energy Physics, Vol. 2009, Issue 04 https://doi.org/10.1088/1126-6708/2009/04/018	journal	April 2009
Type D spacetimes and the Weyl double copy Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel Classical and Quantum Gravity, Vol. 36, Issue 6 https://doi.org/10.1088/1361-6382/ab03e6	journal	February 2019
Solution of the inverse problem of the calculus of variations Douglas, Jesse Transactions of the American Mathematical Society, Vol. 50, Issue 1 https://doi.org/10.1090/S0002-9947-1941-0004740-5	journal	January 1941
Shift symmetries, soft limits, and the double copy beyond leading order González, Mariana Carrillo; Penco, Riccardo; Trodden, Mark Physical Review D, Vol. 102, Issue 10 https://doi.org/10.1103/PhysRevD.102.105011	journal	November 2020
Hidden conformal invariance of scalar effective field theories Cheung, Clifford; Mangan, James; Shen, Chia-Hsien Physical Review D, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevD.102.125009	journal	December 2020
New relations for gauge-theory amplitudes Bern, Z.; Carrasco, J. J. M.; Johansson, H. Physical Review D, Vol. 78, Issue 8 https://doi.org/10.1103/PhysRevD.78.085011	journal	October 2008
Virtuous trees at five- and six-point levels for Yang-Mills theory and gravity Broedel, Johannes; Carrasco, John Joseph M. Physical Review D, Vol. 84, Issue 8 https://doi.org/10.1103/PhysRevD.84.085009	journal	October 2011
Adler’s zero and effective Lagrangians for nonlinearly realized symmetry Low, Ian Physical Review D, Vol. 91, Issue 10 https://doi.org/10.1103/PhysRevD.91.105017	journal	May 2015
Hidden symmetry of the Galileon Hinterbichler, Kurt; Joyce, Austin Physical Review D, Vol. 92, Issue 2 https://doi.org/10.1103/PhysRevD.92.023503	journal	July 2015
Static spherically symmetric Kerr-Schild metrics and implications for the classical double copy Ridgway, Alexander K.; Wise, Mark B. Physical Review D, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevD.94.044023	journal	August 2016
Perturbative Quantum Gravity as a Double Copy of Gauge Theory Bern, Zvi; Carrasco, John Joseph M.; Johansson, Henrik Physical Review Letters, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevLett.105.061602	journal	August 2010
Effective Field Theories from Soft Limits of Scattering Amplitudes Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 114, Issue 22 https://doi.org/10.1103/PhysRevLett.114.221602	journal	June 2015
On-Shell Recursion Relations for Effective Field Theories Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 116, Issue 4 https://doi.org/10.1103/PhysRevLett.116.041601	journal	January 2016
Symmetry for Flavor-Kinematics Duality from an Action Cheung, Clifford; Shen, Chia-Hsien Physical Review Letters, Vol. 118, Issue 12 https://doi.org/10.1103/PhysRevLett.118.121601	journal	March 2017
Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance Arkani-Hamed, Nima; Rodina, Laurentiu; Trnka, Jaroslav Physical Review Letters, Vol. 120, Issue 23 https://doi.org/10.1103/PhysRevLett.120.231602	journal	June 2018
Vector Effective Field Theories from Soft Limits Cheung, Clifford; Kampf, Karol; Novotny, Jiri Physical Review Letters, Vol. 120, Issue 26 https://doi.org/10.1103/PhysRevLett.120.261602	journal	June 2018
Simple Encoding of Higher-Derivative Gauge and Gravity Counterterms Carrasco, John Joseph M.; Rodina, Laurentiu; Yin, Zanpeng Physical Review Letters, Vol. 125, Issue 25 https://doi.org/10.1103/PhysRevLett.125.251602	journal	December 2020
Twistorial Foundation for the Classical Double Copy White, Chris D. Physical Review Letters, Vol. 126, Issue 6 https://doi.org/10.1103/PhysRevLett.126.061602	journal	February 2021
Double Copy Relation in AdS Space Zhou, Xinan Physical Review Letters, Vol. 127, Issue 14 https://doi.org/10.1103/PhysRevLett.127.141601	journal	September 2021
BCJ numerators from differential operator of multidimensional residue Chen, Gang; Wang, Tianheng The European Physical Journal C, Vol. 80, Issue 1 https://doi.org/10.1140/epjc/s10052-019-7604-8	journal	January 2020
TASI Lectures on Scattering Amplitudes Cheung, Clifford 2016 Theoretical Advanced Study Institute in Elementary Particle Physics, Anticipating the Next Discoveries in Particle Physics https://doi.org/10.1142/9789813233348_0008	conference	July 2018

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