Bootstrapping supergravity amplitudes

Consistency requirements on scattering amplitudes can constrain quantum gravity without a perturbative expansion. This talk applies analyticity, crossing and unitarity to maximally supersymmetric gravitational theories in ten and eleven dimensions. It extends bounds from the leading correction to higher-order effective couplings, comparing the allowed regions with string-theory and M-theory predictions. A nearby kink in eleven dimensions suggests a possible route toward characterizing the M-theory scattering matrix through consistency alone.