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BCFW recursion

About: BCFW recursion is a research topic. Over the lifetime, 150 publications have been published within this topic receiving 8807 citations.


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Journal ArticleDOI
TL;DR: A short and direct proof of this recursion relation for tree-level scattering amplitudes based on properties of tree- level amplitudes only is given.
Abstract: Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.

1,605 citations

Journal ArticleDOI
TL;DR: In this article, the authors presented new recursion relations for tree amplitudes in gauge theory that give very compact formulas, in which all particles are on-shell and momentum conservation is preserved.

1,267 citations

Posted Content
TL;DR: In this article, a conjectured universal formula for the finite subleading term in the expansion about the soft limit is given, whose gauge invariance follows from global angular momentum conservation, and the conjecture is non-trivially verified for all tree-level graviton scattering amplitudes using a BCFW recursion relation.
Abstract: The single-soft-graviton limit of any quantum gravity scattering amplitude is given at leading order by the universal Weinberg pole formula. Gauge invariance of the formula follows from global energy-momentum conservation. In this paper evidence is given for a conjectured universal formula for the finite subleading term in the expansion about the soft limit, whose gauge invariance follows from global angular momentum conservation. The conjecture is non-trivially verified for all tree-level graviton scattering amplitudes using a BCFW recursion relation. One hopes to understand this infinity of new soft relations as a Ward identity for a new superrotation Virasoro symmetry of the quantum gravity S-matrix.

513 citations

Journal ArticleDOI
TL;DR: In this paper, a simple physical understanding of amplitudes in this limit is given, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background lightcone gauge.
Abstract: The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in a particular complex direction. This is a very surprising property, since individual Feynman diagrams all diverge at infinite momentum. In this paper we give a simple physical understanding of amplitudes in this limit, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background light-cone gauge. An important role is played by enhanced spin symmetries at infinite momentum-a single copy of a ``Lorentz group for gauge theory and two copies for gravity-which together with Ward identities give a systematic expansion for amplitudes at large momentum. We use this to study tree amplitudes in a wide variety of theories, and in particular demonstrate that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the BCFW recursion relations can be used to compute completely general gluon and graviton tree amplitudes in any number of dimensions. We briefly comment on the implications of these results for computing massive 4D amplitudes by KK reduction, as well understanding the unexpected cancelations that have recently been found in loop-level gravity amplitudes.

363 citations

Journal ArticleDOI
TL;DR: In this article, a supersymmetric recursion relation for tree-level scattering amplitudes in super Yang-Mills was presented, and it was shown that the tree level matrix is covariant under dual superconformal transformations.
Abstract: We present a supersymmetric recursion relation for tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills. Using this recursion relation, we prove that the tree-level $S$ matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyze the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.

348 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20215
20205
201910
20184
201710
201610