The critical ultraviolet behaviour of N=8 supergravity amplitudes

Understand

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.