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266
Tree level recursion relations in general relativity
"... Recently, treelevel recursion relations for scattering amplitudes of gluons in YangMills theory have been derived. In this note we propose a generalization of the recursion relations to treelevel scattering amplitudes of gravitons. We use the relations to derive new simple formulae for all amplit ..."
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Cited by 26 (1 self)
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Recently, treelevel recursion relations for scattering amplitudes of gluons in YangMills theory have been derived. In this note we propose a generalization of the recursion relations to treelevel scattering amplitudes of gravitons. We use the relations to derive new simple formulae for all amplitudes up to six gravitons. In particular, we present an explicit formula for the six graviton nonMHV amplitude. We prove the relations for MHV and nexttoMHV ngraviton amplitudes and for all eightgraviton amplitudes.
All split helicity treelevel gluon amplitudes
, 2006
"... Recently a new recursion relation for treelevel gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admi ..."
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Cited by 20 (1 self)
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Recently a new recursion relation for treelevel gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of âzigzagâ diagrams. We comment on generalizations of this result.
Recursion Relations, Generating Functions, and Unitarity Sums in N = 4 SYM Theory
, 2008
"... We prove that the MHV vertex expansion is valid for any NMHV tree amplitude of N = 4 SYM. The proof uses induction to show that there always exists a complex deformation of three external momenta such that the amplitude falls off at least as fast as 1/z for large z. This validates the generating fun ..."
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Cited by 19 (3 self)
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We prove that the MHV vertex expansion is valid for any NMHV tree amplitude of N = 4 SYM. The proof uses induction to show that there always exists a complex deformation of three external momenta such that the amplitude falls off at least as fast as 1/z for large z. This validates the generating function for npoint NMHV tree amplitudes. We also develop generating functions for antiMHV and antiNMHV amplitudes. As an application, we use these generating functions to evaluate several examples of intermediate state sums on unitarity cuts of 1, 2, 3 and 4loop amplitudes. In a separate analysis, we extend the recent results of arXiv:0808.0504 to prove that there exists a valid 2line shift for any npoint tree amplitude of N = 4 SYM. This implies that
Constructing the TreeLevel YangMills SMatrix Using Complex Factorization
 arXiv:0811.3207 [hepth]. – 24
"... A remarkable connection between BCFW recursion relations and constraints on the Smatrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of fourparticle amplitudes generates nontrivial (but familiar) constraints on threeparticle cou ..."
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Cited by 15 (0 self)
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A remarkable connection between BCFW recursion relations and constraints on the Smatrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of fourparticle amplitudes generates nontrivial (but familiar) constraints on threeparticle coupling constants — these include gauge invariance, the equivalence principle, and the lack of nontrivial couplings for spins> 2. These constraints can also be derived with weaker assumptions, by demanding the existence of fourpoint amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a treelevel Smatrix, and that complex factorization of general BCFW amplitudes follows from the factorization of fourparticle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the threeparticle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the Smatrix is entirely independent of field theory. We analyze the case
Taming tree amplitudes in general relativity
 JHEP
"... Abstract: We give a proof of BCFW recursion relations for all treelevel 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 nexttoMHV amplitudes by one of the authors and P. Svrček in hepth/ ..."
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Cited by 15 (3 self)
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Abstract: We give a proof of BCFW recursion relations for all treelevel 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 nexttoMHV amplitudes by one of the authors and P. Svrček in hepth/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
Complete Six–Gluon Disk Amplitude in Superstring Theory
, 2007
"... We evaluate all nexttomaximal helicity violating (NMHV) sixgluon amplitudes in type I open superstring theory in four dimensions, at the disk level, to all orders in α ′. Although the computation utilizes supersymmetric Ward identities, the result holds for all compactifications, even for those t ..."
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Cited by 15 (7 self)
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We evaluate all nexttomaximal helicity violating (NMHV) sixgluon amplitudes in type I open superstring theory in four dimensions, at the disk level, to all orders in α ′. Although the computation utilizes supersymmetric Ward identities, the result holds for all compactifications, even for those that break supersymmetry and is completely modelindependent. Together with the maximally helicity violating (MHV) amplitudes presented in the previous work, our results provide the complete sixgluon disk amplitude
Multi gluon collinear limits from mhv amplitudes
"... Abstract: We consider the multicollinear limit of multigluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative hel ..."
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Cited by 14 (2 self)
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Abstract: We consider the multicollinear limit of multigluon QCD amplitudes at tree level. We use the MHV rules for constructing colour ordered tree amplitudes and the general collinear factorization formula to derive timelike splitting functions that are valid for specific numbers of negative helicity gluons and an arbitrary number of positive helicity gluons (or vice versa). As an example we present new results describing the collinear limits of up to six gluons.