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Is \(\mathcal N=8\) supergravity ultraviolet finite? (English) Zbl 1248.83136

Summary: Conventional wisdom holds that no four-dimensional gravity field theory can be ultraviolet finite. This understanding is based mainly on power counting. Recent studies confirm that one-loop \(N=8\) supergravity amplitudes satisfy the so-called “no-triangle hypothesis”, which states that triangle and bubble integrals cancel from these amplitudes. A consequence of this hypothesis is that for any number of external legs, at one loop \(N=8\) supergravity and \(N=4\) super-Yang-Mills have identical superficial degrees of ultraviolet behavior in \(D\) dimensions. We describe how the unitarity method allows us to promote these one-loop cancellations to higher loops, suggesting that previous power counts were too conservative. We discuss higher-loop evidence suggesting that \(N=8\) supergravity has the same degree of divergence as \(N=4\) super-Yang-Mills theory and is ultraviolet finite in four dimensions. We comment on calculations needed to reinforce this proposal, which are feasible using the unitarity method.

MSC:

83E50 Supergravity
81T18 Feynman diagrams
81T60 Supersymmetric field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
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