Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand through three loops at four points and at one loop for all multiplicities.
Unexpected Cancellations in Gravity Theories
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abstract
Recent computations of scattering amplitudes show that N=8 supergravity is surprisingly well behaved in the ultraviolet and may even be ultraviolet finite in perturbation theory. The novel cancellations necessary for ultraviolet finiteness first appear at one loop in the guise of the "no-triangle hypothesis". We study one-loop amplitudes in pure Einstein gravity and point out the existence of cancellations similar to those found previously in N=8 supergravity. These cancellations go beyond those found in the one-loop effective action. Using unitarity, this suggests that generic theories of quantum gravity based on the Einstein-Hilbert action may be better behaved in the ultraviolet at higher loops than suggested by naive power counting, though without additional (supersymmetric) cancellations they diverge. We comment on future studies that should be performed to support this proposal.
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Gravity loop integrands from the ultraviolet
Four-dimensional N=8 supergravity loop integrands scale one power better at infinity than general-D power-counting predicts, and this homogeneous scaling combined with BCFW behavior uniquely fixes the integrand through three loops at four points and at one loop for all multiplicities.