Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory

Britto, Ruth; Cachazo, Freddy; Feng, Bo; Witten, Edward

doi:10.1103/physrevlett.94.181602

Cited by 1,399 publications

(2,465 citation statements)

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“…However, it is known that in gauge theory, deformed amplitudes also vanish at infinity if the helicities (h i , h j ) of the deformed gluons are (−, −) or (+, +) [11]. It would be interesting to prove a similar statement for General Relativity.…”

Section: Ward Identitiesmentioning

confidence: 96%

“…One in which an amplitude is given as a sum of terms containing the product of two physical on-shell amplitudes where the momenta of only two gravitons have been complexified. These recursion relations, originally discovered in [7] in gauge theory, were proven using the power of complex analysis in [11]. The BCFW construction opened up the possibility for using complex analysis in many other situations.…”

Section: Conclusion and Further Directionsmentioning

confidence: 99%

“…These recursion relations were inspired by [8,9] and reproduced very compact results obtained in [10] by studying the IR behavior of N = 4 one-loop amplitudes. A simple and elegant proof of the relations was later given by the same authors in collaboration with Witten in [11]. The proof is constructive and gives rise to a method using the power of complex analysis for deriving similar relations in any theory where physical singularities are well understood.…”

Section: Introductionmentioning

confidence: 99%

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Taming tree amplitudes in general relativity

Benincasa

Boucher-Veronneau

Cachazo

2007

J. High Energy Phys.

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164

260

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Abstract:We give a proof of BCFW recursion relations for all tree-level amplitudes of gravitons in General Relativity. The proof follows the same basic steps as in the BCFW construction and it is an extension of the one given for next-to-MHV amplitudes by one of the authors and P. Svrček in hep-th/0502160. The main obstacle to overcome is to prove that deformed graviton amplitudes vanish as the complex variable parameterizing the deformation is taken to infinity. This step is done by first proving an auxiliary recursion relation where the vanishing at infinity follows directly from a Feynman diagram analysis. The auxiliary recursion relation gives rise to a representation of gravity amplitudes where the vanishing under the BCFW deformation can be directly proven. Since all our steps are based only on Feynman diagrams, our proof completely establishes the validity of BCFW recursion relations. This means that results in the literature that were derived assuming their validity become true statements.

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Section: Ward Identitiesmentioning

confidence: 96%

Section: Conclusion and Further Directionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Taming tree amplitudes in general relativity

Benincasa

Boucher-Veronneau

Cachazo

2007

J. High Energy Phys.

Self Cite

164

260

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“…Order (α ′ ) 4 and beyond? Using our current Mathematica implementation, it seems difficult to continue our computer calculations beyond d = 6.…”

Section: Jhep11(2008)015mentioning

confidence: 99%

“…This was mainly inspired by Witten's twistor string proposal [1] and includes at tree level the formulation of new Feynman-like rules [2] as well as new recursive relations [3,4]. Historically, the development of new technology in four-dimensional Yang-Mills theory was often motivated from string theory.…”

Section: Introductionmentioning

confidence: 99%

MHV, CSW and BCFW: field theory structures in string theory amplitudes

Boels

Larsen

Obers³

et al. 2008

J. High Energy Phys.

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Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α ′ -corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α ′3 -correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.

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(0,2) Gauged linear sigma model on supermanifold

Okame

Hayashi

2009

Ann. Phys.

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We construct (0, 2), D = 2 gauged linear sigma model on supermanifold with both an Abelian and non-Abelian gauge symmetry. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operatorÛ for the Abelian gauge group. TheÛ operator provides consistency conditions for satisfying the SUSY invariance. On the other hand, it is not essential to introduce a similar operator in order to check the exact SUSY invariance of the Lagrangian density of non-Abelian model, contrary to the Abelian one. However, we still need a new operator in order to define the (0,2) chirality conditions for the (0,2) chiral superfields. The operator U a can be defined from the conditions assuring the (0,2) supersymmetric invariance of the Lagrangian density in superfield formalism for the (0,2) U(N) gauged linear sigma model.We found consistency conditions for the Abelian gauge group which assure (0,2) supersymmetric invariance of Lagrangian density and agree with (0,2) chirality conditions for the superpotential. The supermanifold M m|n becomes the super weighted complex projective space W CP m−1|n in the U(1) case, which is considered as an example of a Calabi-Yau supermanifold. The superpotential W (φ, ξ) for the non-Abelian gauge group satisfies more complex condition for the SU(N) part, except the U(1) part of U(N), but does not satisfy a quasi-homogeneous condition. This fact implies the need for taking care of constructing the Calabi-Yau supermanifold in the SU(N) part. Because more stringent restrictions are imposed on the form of the superpotential than in the U(1) case, the superpotential seems to define a certain kind of new supermanifolds which we cannot identify exactly with one of the mathematically well defined objects.

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Direct Proof of the Tree-Level Scattering Amplitude Recursion Relation in Yang-Mills Theory

Cited by 1,399 publications

References 13 publications

Taming tree amplitudes in general relativity

Taming tree amplitudes in general relativity

MHV, CSW and BCFW: field theory structures in string theory amplitudes

(0,2) Gauged linear sigma model on supermanifold

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