Is N=8 Supergravity Ultraviolet Finite?

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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 ... continued below

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7 pages

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Bern, Zvi; Dixon, Lance J. & Roiban, Radu November 15, 2006.

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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.

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7 pages

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  • Journal Name: Physics Letters B

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  • Report No.: SLAC-PUB-12187
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 895263
  • Archival Resource Key: ark:/67531/metadc891297

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  • November 15, 2006

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  • Sept. 22, 2016, 2:13 a.m.

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  • Dec. 7, 2016, 3:50 p.m.

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Bern, Zvi; Dixon, Lance J. & Roiban, Radu. Is N=8 Supergravity Ultraviolet Finite?, article, November 15, 2006; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc891297/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.