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The critical ultraviolet behaviour of N=8 supergravity amplitudes
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We analyze the critical ultraviolet behaviour of the four-graviton amplitude in N=8 supergravity to all order in perturbation. We use the Bern-Carrasco-Johansson diagrammatic expansion for N=8 supergravity multiloop amplitudes, where numerator factors are squares of the Lorentz factor of N=4 super-Yang-Mills amplitudes, and the analysis of the critical ultraviolet behaviour of the multiloop four-gluon amplitudes in the single- and double-trace sectors. We argue this implies that the superficial ultraviolet behaviour of the four-graviton N=8 amplitudes from four-loop order is determined by the factorization the k^8 R^4 operator. This leads to a seven-loop logarithmic divergence in the four-graviton amplitude in four dimensions.
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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 throug...
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