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We analyze the critical ultraviolet behaviour of the four-graviton amplitudein N=8 supergravity to all order in perturbation. We use theBern-Carrasco-Johansson diagrammatic expansion for N=8 supergravity multiloopamplitudes, where numerator factors are squares of the Lorentz factor of N=4super-Yang-Mills amplitudes, and the analysis of the critical ultravioletbehaviour of the multiloop four-gluon amplitudes in the single- anddouble-trace sectors. We argue this implies that the superficial ultravioletbehaviour of the four-graviton N=8 amplitudes from four-loop order isdetermined by the factorization the k^8 R^4 operator. This leads to aseven-loop logarithmic divergence in the four-graviton amplitude in fourdimensions.

The critical ultraviolet behaviour of N=8 supergravity amplitudes