Three-Loop Superfiniteness of N=8 Supergravity

Abstract

We construct the three-loop four-point amplitude of N=8 supergravity using the unitarity method. The amplitude is ultraviolet finite in four dimensions. Novel cancellations, not predicted by traditional superspace power-counting arguments, render its degree of divergence in D dimensions to be no worse than that of N=4 super-Yang-Mills theory -- a finite theory in four dimensions. Similar cancellations can be identified at all loop orders in certain unitarity cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of quantum gravity.

5 pages, 4 figures. In v2 references and minor clarifications added

References in corpus (9)

• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Duality and higher derivative terms in M theory
• Is N = 8 Supergravity Ultraviolet Finite?
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• Non-renormalisation Conditions in Type II String Theory and Maximal Supergravity
• The No-Triangle Hypothesis for N=8 Supergravity
• Supersymmetry counterterms revisited

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