Abstract
Recently, a BCJ dual of the color-ordered formula for Yang-Mills amplitude was proposed, where the dual-trace factor satisfies cyclic symmetry and KK-relation. In this paper, we present a systematic construction of the dual-trace factor based on its proposed relations to kinematic numerators in dual-DDM form. We show that the construction presented respects relabeling symmetry. In addition, we show that using relabeling symmetry as conditions, the same construction can be solved independently.
Similar content being viewed by others
References
Z. Bern, J. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
R. Kleiss and H. Kuijf, Multi - gluon cross-sections and five jet production at hadron colliders, Nucl. Phys. B 312 (1989) 616 [INSPIRE].
V. Del Duca, L.J. Dixon and F. Maltoni, New color decompositions for gauge amplitudes at tree and loop level, Nucl. Phys. B 571 (2000) 51 [hep-ph/9910563] [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Minimal Basis for Gauge Theory Amplitudes, Phys. Rev. Lett. 103 (2009) 161602 [arXiv:0907.1425] [INSPIRE].
S. Stieberger, Open and Closed vs. Pure Open String Disk Amplitudes, arXiv:0907.2211 [INSPIRE].
S.H. Henry Tye and Y. Zhang, Dual Identities inside the Gluon and the Graviton Scattering Amplitudes, JHEP 06 (2010) 071 [Erratum ibid. 1104 (2011) 114] [arXiv:1003.1732] [INSPIRE].
B. Feng, R. Huang and Y. Jia, Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program, Phys. Lett. B 695 (2011) 350 [arXiv:1004.3417] [INSPIRE].
Y. Jia, R. Huang and C.-Y. Liu, U (1)-decoupling, KK and BCJ relations in \( \mathcal{N} \) = 4 SYM, Phys. Rev. D 82 (2010) 065001 [arXiv:1005.1821] [INSPIRE].
H. Tye and Y. Zhang, Remarks on the identities of gluon tree amplitudes, Phys. Rev. D 82 (2010) 087702 [arXiv:1007.0597] [INSPIRE].
Y.-X. Chen, Y.-J. Du and B. Feng, A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory, JHEP 02 (2011) 112 [arXiv:1101.0009] [INSPIRE].
H. Kawai, D. Lewellen and S. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Gravity and Yang-Mills Amplitude Relations, Phys. Rev. D 82 (2010) 107702 [arXiv:1005.4367] [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, New Identities among Gauge Theory Amplitudes, Phys. Lett. B 691 (2010) 268 [arXiv:1006.3214] [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard, B. Feng and T. Sondergaard, Proof of Gravity and Yang-Mills Amplitude Relations, JHEP 09 (2010) 067 [arXiv:1007.3111] [INSPIRE].
B. Feng and S. He, KLT and New Relations for N = 8 SUGRA and N = 4 SYM, JHEP 09 (2010) 043 [arXiv:1007.0055] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
Z. Bern, J. Carrasco, L. Dixon, H. Johansson and R. Roiban, Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes, Phys. Rev. D 85 (2012) 105014 [arXiv:1201.5366] [INSPIRE].
Z. Bern, C. Boucher-Veronneau and H. Johansson, N ≥ 4 Supergravity Amplitudes from Gauge Theory at One Loop, Phys. Rev. D 84 (2011) 105035 [arXiv:1107.1935] [INSPIRE].
C. Boucher-Veronneau and L. Dixon, N ≥ 4 Supergravity Amplitudes from Gauge Theory at Two Loops, JHEP 12 (2011) 046 [arXiv:1110.1132] [INSPIRE].
S.G. Naculich, H. Nastase and H.J. Schnitzer, Linear relations between N ≥ 4 supergravity and subleading-color SYM amplitudes, JHEP 01 (2012) 041 [arXiv:1111.1675] [INSPIRE].
S. Oxburgh and C. White, BCJ duality and the double copy in the soft limit, JHEP 02 (2013) 127 [arXiv:1210.1110] [INSPIRE].
J.J.M. Carrasco, M. Chiodaroli, M. Gnaydin and R. Roiban, One-loop four-point amplitudes in pure and matter-coupled N ≤ 4 supergravity, JHEP 03 (2013) 056 [arXiv:1212.1146] [INSPIRE].
R.H. Boels, R.S. Isermann, R. Monteiro and D. O’Connell, Colour-Kinematics Duality for One-Loop Rational Amplitudes, JHEP 04 (2013) 107 [arXiv:1301.4165] [INSPIRE].
N.E.J. Bjerrum-Bohr, T. Dennen, R. Monteiro and D. O’Connell, Integrand Oxidation and One-Loop Colour-Dual Numerators in N = 4 Gauge Theory, arXiv:1303.2913 [INSPIRE].
Z. Bern, S. Davies, T. Dennen, Y.-t. Huang and J. Nohle, Color-Kinematics Duality for Pure Yang-Mills and Gravity at One and Two Loops, arXiv:1303.6605 [INSPIRE].
C.R. Mafra, O. Schlotterer and S. Stieberger, Explicit BCJ Numerators from Pure Spinors, JHEP 07 (2011) 092 [arXiv:1104.5224] [INSPIRE].
R. Monteiro and D. O’Connell, The Kinematic Algebra From the Self-Dual Sector, JHEP 07 (2011) 007 [arXiv:1105.2565] [INSPIRE].
N. Bjerrum-Bohr, P.H. Damgaard, R. Monteiro and D. O’Connell, Algebras for Amplitudes, JHEP 06 (2012) 061 [arXiv:1203.0944] [INSPIRE].
C.-H. Fu, Y.-J. Du and B. Feng, An algebraic approach to BCJ numerators, JHEP 03 (2013) 050 [arXiv:1212.6168] [INSPIRE].
Y.-J. Du, B. Feng and C.-H. Fu, BCJ Relation of Color Scalar Theory and KLT Relation of Gauge Theory, JHEP 08 (2011) 129 [arXiv:1105.3503] [INSPIRE].
Z. Bern, A. De Freitas and H. Wong, On the coupling of gravitons to matter, Phys. Rev. Lett. 84 (2000) 3531 [hep-th/9912033] [INSPIRE].
Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Gravity as the Square of Gauge Theory, Phys. Rev. D 82 (2010) 065003 [arXiv:1004.0693] [INSPIRE].
Z. Bern and T. Dennen, A Color Dual Form for Gauge-Theory Amplitudes, Phys. Rev. Lett. 107 (2011) 081601 [arXiv:1103.0312] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1304.2978
Rights and permissions
About this article
Cite this article
Du, YJ., Feng, B. & Fu, CH. The construction of dual-trace factor in Yang-Mills theory. J. High Energ. Phys. 2013, 57 (2013). https://doi.org/10.1007/JHEP07(2013)057
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2013)057