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I think we should interpret these loop divergences,
not as a break down of the supergravity theories,
but as a break down of naive perturbation theory.
In gauge theories, we know that perturbation theory breaks down at strong coupling.
In quantum gravity, the role of the gauge coupling,
is played by the energy of a particle.
In a quantum loop one integrates overů So one would expect perturbation theory, to break down.