Tree level recursion relations in general relativity

By F. Cachazo, Peter Svrček. 2005

162 citations recorded by the source corpus.

Recently, tree-level recursion relations for scattering amplitudes of gluons in Yang-Mills theory have been derived. In this note we propose a generalization of the recursion relations to tree-level 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 non-MHV amplitude. We prove the relations for MHV and next-to-MHV n-graviton amplitudes and for all eight-graviton amplitudes.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a9c5d6fe57b3a9c6e43e5a015fa4ebbf728dd5a2

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Citations in the corpus

Taming tree amplitudes in general relativity (2007, methodology): “In [22], it was shown that the BGK formula vanishes at infinity for any n1 under the (+,−) deformation.”
A direct proof of the CSW rules (2005, methodology): “The methods of BCFW recursion have been applied and extended with great success to both tree-level calculations in Yang–Mills and other theories [41, 42, 43, 44, 45, 46, 47, 48] as well as one-loop calculations [49, 50, 51, 52], and, in some of these cases, been merged with technology such as…”
Recursion relations for gauge theory amplitudes with massive particles. (2005, background): “Similar recursion relations with three or more marked particles have been recently considered in [21, 22, 38].”
Consistency Conditions on the S-Matrix of Massless Particles (2007, background): “Examples of fully constructible theories are Yang-Mills [19] and General Relativity [20, 21, 22] (the fact that cubic couplings could play a key role in Yang-Mills theory and General Relativity was already understood in [23, 24]).”
Generating tree amplitudes in Script N = 4 SYM and Script N = 8 SG (2008, background): “On-shell tree amplitudes in gauge theory and gravity are best expressed using the spinor helicity formalism and are most easily obtained from the modern form of recursion relations [6, 7, 8, 9] which relate n-point amplitudes to those for smaller values of n.”
Evidence for a New Soft Graviton Theorem (2014, background): “(68) In order to compare to the six-point amplitude we take the explicit form given in [22] as M6 = D1 +D1 flip +D2 +D3 +D3 flip +D6 (69) with(6) D1 = 〈23〉〈1|2 + 3|4]7(〈1|2 + 3|4]〈5|3 + 4|2][51]− [12][45]〈51〉s234) 〈15〉〈16〉[23][34]2〈56〉s234〈1|3 + 4|2]〈5|3 + 4|2]〈5|2 + 3|4]〈6|3 + 4|2]〈6|2 + 3|4] +(1 ↔”