A recursion relation for gravity amplitudes

By J. Bedford, A. Brandhuber, B. Spence, G. Travaglini. 2005

193 citations recorded by the source corpus.

Abstract Britto, Cachazo and Feng have recently derived a recursion relation for tree-level scattering amplitudes in Yang–Mills. This relation has a bilinear structure inherited from factorisation on multi-particle poles of the scattering amplitudes—a rather generic feature of field theory. Motivated by this, we propose a new recursion relation for scattering amplitudes of gravitons at tree level. Using this, we derive a new general formula for the MHV tree-level scattering amplitude for n gravitons. Finally, we comment on the existence of recursion relations in general field theories.

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Citations in the corpus

Amplitudes and Spinor-Helicity in Six Dimensions (2009, background): “First proposed for tree-level YM amplitudes [9, 10], recursion relations were later derived for gravity [12, 13] and eventually found to be a quite generic property of tree amplitudes in quantum field theories in arbitrary dimensions [14, 15].”
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]).”
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 unitar”
Taming tree amplitudes in general relativity (2007, methodology): “In [21], the desired behavior was checked for MHV amplitudes up to n < 11 under the (−,−) deformation using the BGK formula [23].”
Tree level recursion relations in general relativity (2005, unknown): “Note: After this work was completed, [19] appeared which has some overlap with our results.”
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].”
Generating tree amplitudes in Script N = 4 SYM and Script N = 8 SG (2008, background): “However there are now more diagrams of the type in figure 2(a), namely the n−2 diagrams containing cyclic permutations of the positive helicity lines [8].”
Evidence for a New Soft Graviton Theorem (2014, background): “D3 = 〈13〉8[14][56]7(〈23〉〈56〉[62]〈1|3+ 4|5] + 〈35〉[56]〈62〉〈1|3 + 4|2]) 〈14〉[25][26]〈34〉2s134〈1|3 + 4|2]〈1|3 + 4|5]〈1|3 + 4|6]〈3|1 + 4|2]〈3|1 + 4|5]〈3|1 + 4|6] (1 ↔ 2), (72) and D6 = 〈12〉[56]〈3|1 + 2|4]8 [21][14][24]〈35〉〈36〉〈56〉s124〈5|1 + 2|4]〈6|1 + 2|4]〈3|5 + 6|1]〈3|5 + 6|2] .”