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Multi-leg one-loop gravity amplitudes from gauge theory. (English) Zbl 0953.83006

Summary: 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 \(n\leqslant 6\), 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 \(n\leqslant 6 N=8\) 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.

MSC:

83C45 Quantization of the gravitational field
81T13 Yang-Mills and other gauge theories in quantum field theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
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