Gauge amplitude identities by on-shell recursion relation in S-matrix program

By Bo Feng, Rijun Huang, Yin Jia. 2010

222 citations recorded by the source corpus.

Abstract Using only the Britto–Cachazo–Feng–Witten (BCFW) on-shell recursion relation we prove color-order reversed relation, U ( 1 ) -decoupling relation, Kleiss–Kuijf (KK) relation and Bern–Carrasco–Johansson (BCJ) relation for color-ordered gauge amplitude in the framework of S-matrix program without relying on Lagrangian description. Our derivation is the first pure field theory proof of the new discovered BCJ identity, which substantially reduces the color-ordered basis from ( n − 2 ) ! to ( n − 3 ) ! . Our proof gives also its physical interpretation as the mysterious bonus relation with 1 z 2 behavior under suitable on-shell deformation for no adjacent pair.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/238013dee96b6c48d2f71f40649338fbd04c4abe

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Citations in the corpus

Colour-Kinematics duality for one-loop rational amplitudes (2013, methodology): “J (1) 3 (+ + +) = (− )(1− )(4π) ∫ dD+4L (2π)D+4 [12]2 〈12〉2 X(l3, 3) 2”
The double copy: Bremsstrahlung and accelerating black holes (2016, background): “The validity of the BCJ double copy and the existence of colour-dual numerators has been proven at tree-level [5–13] (where it is equivalent to the KLT relations [1]).”
The classical double copy for Taub–NUT spacetime (2015, background): “This itself relies on a certain relationship (BCJ duality) being made manifest in the gauge theory, and is known to be true at tree-level [2,4–10], where it is equivalent to the KLT relations of [11].”
Color-kinematics duality for QCD amplitudes (2015, background): “The BCJ amplitude relations, which are a consequence of the duality [31] but can be proven by other means [71, 72, 85], have in a few cases been shown to generalize to massive amplitudes.”
The momentum kernel of gauge and gravity theories (2010, methodology): “These BCJ-relations, which also hold when including matter [6, 7], turn out to be the field theory limit of monodromy relations in string theory [8] (see also [9, 10]).”
One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts (2011, methodology): “They have been proven first using the field theory limit of monodromy relations in string theory [91] and later derived using BCFW recursion relations [92, 93](8).”