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Fundamental BCJ Relation in N=4 SYM From The Connected Formulation · Around

2012

Fundamental BCJ Relation in N=4 SYM From The Connected Formulation

Cachazo, Freddy

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Understand

Tree-level amplitudes in N=4 SYM can be decomposed into partial or color-ordered amplitudes.

Identities relating various partial amplitudes have been known since the 80's.
They are Kleiss-Kuijf (KK) identities.
In 2008, Bern, Carrasco and Johansson (BCJ) introduced a new set of identities which reduce the number of independent partial amplitudes to (n-3)!.

Built on

H. Kawai, D. C. Lewellen and S. H. H. Tye, “A Relation Between Tree Amplitudes of Closed and Open Strings,” Nucl. Phys. B 269
1986
Earlier work this paper cites.
R. Kleiss and H. Kuijf, “Multi - Gluon Cross-sections And Five Jet Production At Hadron Colliders,” Nucl. Phys. B 312
1989
Earlier work this paper cites.
For a review see: L. J. Dixon, “Calculating Scattering Amplitudes Efficiently,” In *Boulder 1995, QCD and beyond* 539-582 [hep-ph/9601359]
1995
Earlier work this paper cites.
E. Witten, “Perturbative Gauge Theory as a String Theory in Twistor Space,” Commun. Math. Phys
2004
Earlier work this paper cites.

Similar

R. Roiban, M. Spradlin and A. Volovich, “On the Tree Level S Matrix of Yang-Mills Theory,” Phys. Rev. D 70
2004
Cited alongside, same era.
Z. Bern, J. J. M. Carrasco and H. Johansson, “New Relations for Gauge-Theory Amplitudes,” Phys. Rev. D 78
Original
2008
Cited alongside, same era.
N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, “A Duality for The S-Matrix,” 2009, arXiv:0907.5418 [hep-th]
Original
2009
Cited alongside, same era.
L. J. Mason and D. Skinner, “Dual Superconformal Invariance, Momentum Twistors and Grassmannians,” JHEP 0911
Original
2009
Cited alongside, same era.
B. Feng and M. Luo, “An Introduction to On-shell Recursion Relations,” arXiv:1111.5759 [hep-th]
Original
Cited in the paper.

Then

N. Arkani-Hamed, F. Cachazo, and C. Cheung, “The Grassmannian Origin Of Dual Superconformal Invariance,” 2009, arXiv:0909.0483 [hep-th]
Original
2009
Later among the works it cites.
H. Tye and Y. Zhang, “Comment on the Identities of the Gluon Tree Amplitudes,” Phys. Rev. D 82
Original
2010
Later among the works it cites.
N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka, “Unification of Residues and Grassmannian Dualities,” JHEP 1101
Original
2011
Later among the works it cites.
See chapter V of: N. Beisert, C. Ahn, L. F. Alday, Z. Bajnok, J. M. Drummond, L. Freyhult, N. Gromov and R. A. Janik et al
Original
2012
Closest in time.

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