TY - JOUR

T1 - Is N = 8 supergravity ultraviolet finite?

AU - Bern, Z.

AU - Dixon, L. J.

AU - Roiban, R.

N1 - Funding Information:
We thank Nathan Berkovits, Emil Bjerrum-Bohr, John Joseph Carrasco, Dave Dunbar, Michael Green, Harald Ita, Henrik Johansson, David Kosower, Arkady Tseytlin and Pierre Vanhove for helpful discussions. This research was supported by the US Department of Energy under contracts DE-FG03-91ER40662 and DE-AC02-76SF00515, and the National Science Foundation under grant PHY-0608114.

PY - 2007/1/18

Y1 - 2007/1/18

N2 - 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.

AB - 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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U2 - 10.1016/j.physletb.2006.11.030

DO - 10.1016/j.physletb.2006.11.030

M3 - Article

AN - SCOPUS:33845636143

SN - 0370-2693

VL - 644

SP - 265

EP - 271

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 4

ER -