Is N = 8 supergravity ultraviolet finite?

Z. Bern, L. J. Dixon, R. Roiban

Research output: Contribution to journalArticlepeer-review

145 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)265-271
Number of pages7
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number4
StatePublished - Jan 18 2007

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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