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On Primary Relations at Tree-level in String Theory and Field Theory · Around

2011

On Primary Relations at Tree-level in String Theory and Field Theory

Ma, Qian, Du, Yi-Jian, Chen, Yi-Xin

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By the use of cyclic symmetry, KK relations and BCJ relations, one can reduce the number of independent $N$-point color-ordered tree amplitudes in gauge theory and string theory from $N!$ to $(N-3)!$.

In this paper, we investigate these relations at tree-level in both string theory and field theory.
We will show that there are two primary relations.
All other relations can be generated by the primary relations.

Built on

Y. X. Chen, Y. J. Du and B. Feng, “On tree amplitudes with gluons coupled to gravitons,” JHEP 1101
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Similar

T. Sondergaard, “New Relations for Gauge-Theory Amplitudes with Matter,” Nucl. Phys. B 821
Original
2009
Cited alongside, same era.
N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard and P. Vanhove, “Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes,” JHEP 1006
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2010
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Y. Jia, R. Huang and C. Y. Liu, “ U ⁡ ( 1 ) U(1) -decoupling, KK and BCJ relations in 𝒩 = 4 \mathcal{N}=4 SYM,” Phys. Rev. D 82
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2010
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N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng and T. Sondergaard, “Gravity and Yang-Mills Amplitude Relations,” Phys. Rev. D 82
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2010
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N. E. J. Bjerrum-Bohr, P. H. Damgaard, B. Feng and T. Sondergaard, “New Identities among Gauge Theory Amplitudes,” Phys. Lett. B 691

Then

C. R. Mafra, “Simplifying the Tree-level Superstring Massless Five-point Amplitude,” JHEP 1001
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2010
Later among the works it cites.
B. Feng, J. Wang, Y. Wang and Z. Zhang, “BCFW Recursion Relation with Nonzero Boundary Contribution,” JHEP 1001
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2010
Later among the works it cites.
B. Feng and C. Y. Liu, “A Note on the boundary contribution with bad deformation in gauge theory,” JHEP 1007
Original
2010
Later among the works it cites.
N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard and P. Vanhove, “The Momentum Kernel of Gauge and Gravity Theories,” JHEP 1101
Original
2011
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B. Feng, R. Huang and Y. Jia, “Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program,” Phys. Lett. B 695

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