We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional $N=8$ supergravity might be ultraviolet finite up to eight loops. We similarly argue that the $h$-loop $M$-graviton amplitude might be finite for $h<7+M/2$.

• Received 18 January 2007

DOI:https://doi.org/10.1103/PhysRevLett.98.131602