A recursion relation for gravity amplitudes

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.

Taming tree amplitudes in general relativity

“…Therefore, the amplitude still vanishes in this case. In [21], a very nice compact formula was conjectured for MHV amplitudes of gravitons by assuming the validity of BCFW recursion relations obtained via a deformation of the two negative helicity gravitons. Our proof and the discussion in this section validates the recursion relations used to construct the all multiplicity ansatz.…”

“…Our proof and the discussion in this section validates the recursion relations used to construct the all multiplicity ansatz. It would be highly desirable to show that the formula proposed by Bedford et al [21] does indeed satisfy the recursion relations. The formula is explicitly given by…”

“…The possibility of the existence of BCFW recursion relations in General Relativity was first investigated in [21,22]. There it was pointed out that the main obstacle to establish the validity of the recursion relations is to prove that deformed amplitudes vanish at infinity while individual Feynman diagrams diverge.…”

“…There it was pointed out that the main obstacle to establish the validity of the recursion relations is to prove that deformed amplitudes vanish at infinity while individual Feynman diagrams diverge. In [21], the desired behavior was checked for MHV amplitudes up to n < 11 under the (−, −) deformation using the BGK formula [23]. In [22], it was shown that the BGK formula vanishes at infinity for any n 1 under the (+, −) deformation.…”

MHV-vertices for gravity amplitudes

“…Most of the above developments have been made for gauge theory amplitudes. The existence of a BCFW recusion relation for gravity amplitudes was strongly supported in [24,25], and in this article we construct a CSW approach using the newly established shift (1.6) under the assumption that gravity amplitudes are sufficiently well behaved for large values of z in (1.6).…”