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

Gauge amplitude identities by on-shell recursion relation in S-matrix program,10.1016/j.physletb.2010.11.011,Physics Letters B,Bo Feng,Rijun Huang,Yin

Gauge amplitude identities by on-shell recursion relation in S-matrix program   (Citations: 12)
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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 1z2 behavior under suitable on-shell deformation for no adjacent pair.
Journal: Physics Letters B - PHYS LETT B , vol. 695, no. 1, pp. 350-353, 2011
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    • ...The new discovered fundamental BCJ relation (as well as KK relation) and KLT relation have been proved by Britto-Cachazo-Feng-Witten(BCFW) on-shell recursion relation [18, 19] along the line of S-matrix program [20, 21] in [11, 13] and [14–17]...
    • ...The (n − 3)! expression can also be derived only from the fundamental BCJ relation and KK relation [11]...
    • ...Though we can always express a given amplitude in the minimal basis by using the fundamental BCJ relation and KK relation [11], it is difficult to derive a general expression of the minimal-basis expansion [2] in this way...
    • ...To show this is true, there are two possible ways to go. The first way is to use the fundamental BCJ relation recursively [11], while the second way, the BCFW recursion relation [18, 19]...
    • ...It is worth to notice that the method of proof is similar to the one used for the fundamental BCJ relation [11]...

    Yi-Xin Chenet al. A proof of the explicit minimal-basis expansion of tree amplitudes in ...

    • ...monodromy relations in string theory [18] (see also [21–26] and [27–29] for an alternative string theory approach), but have now also been proven using pure field theory [30, 31]...

    N. E. J. Bjerrum-Bohret al. Monodromy-like relations for finite loop amplitudes

    • ...The proof are similarly with in the pure gluon case [7]...
    • ...To see this, we should count the number of terms in each expression as in [7]...

    Yi-Xin Chenet al. On tree amplitudes with gluons coupled to gravitons

    • ...This leads one to suspect for instance that loop level relations for integrands like those conjectured in [45] between gauge theory and gravity can be proven just as the tree level version of these relations [46] can be proven from non-adjacent BCFW shifts [47] (see also [48])...

    Rutger H. Boelset al. On BCFW shifts of integrands and integrals

    • ...In a series of papers, Bern and his collaborators [1–3], and others using string theory insights [4] or through the use of the BCFW [5] recursion relations 1 [9], obtained some very...
    • ...A related observation (see [4, 9]) is that the Kleiss-Kuijf amplitudes matrix A obeys a set of constraints which can be summarized by the following equation: �...

    Diana Vamanet al. Constraints and generalized gauge transformations on tree-level gluon ...

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