Multi-leg one-loop gravity amplitudes from gauge theory

By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maxim ally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plu s' helicity amplitudes in gravity with any minimally coupled massless matte r content. The all-plus amplitudes correspond to self-dual field configurat ions and vanish in supersymmetric theories. We make use of the tree-level K awai-Lewellen-Tye (KLT) relations between open and closed string theory amp litudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n less than or equal to 6, we determine t he all-plus amplitudes explicitly from their unitarity cuts. The KLT relati ons, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 s uper-Yang-Mills theory. The gravitational version of the relation lets us d etermine the n less than or equal to 6 N = 8 supergravity amplitudes from t he all-plus gravity amplitudes. We infer the two series of amplitudes for a ll n from their soft and collinear properties, which can also be derived fr om gauge theory using the KLT relations. (C) 1999 Published by Elsevier Sci ence B.V.