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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 `maximally helicity-violating' amplitudes in $N=8$ supergravity, and the `all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For $n\le 6$, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, 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 $N=4$ super-Yang-Mills theory. The gravitational version of the relation lets us determine the $n\le6$ $N=8$ supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all $n$ from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations. \vskip .3 cm \noindent {\it PACS:} 04.50.+h; 04.65+e;04.60.-m\\ {\it Keywords:} Unitarity; Cutting; Supersymmetry; Supergravity; One-loop

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