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Three-Loop Superfiniteness of N=8 Supergravity

Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower, R. Roiban

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.

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.

Paper Structure

This paper contains 3 equations, 2 figures, 1 table.

Figures (2)

  • Figure 1: Generalized cuts used to determine the three-loop four-point amplitude.
  • Figure 2: Loop integrals appearing in both ${{\cal N}=4}$ gauge-theory and ${{\cal N}=8}$ supergravity three-loop four-point amplitudes. The integrals are specified by combining the diagrams' propagators with numerator factors given in table \ref{['NumeratorTable']}.