# Divergence in Supergravity

I'm not familiar with supergravity so here's my question: I've heard in talks that if one finds divergence for five-loop 4-graviton scattering amplitudes in five dimensions this translates to a divergence in $D=4$ at seven loops.

How do I see this? What's the argument behind this?

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This looks very much like the "experimental" bound that you can find in the paper by Zvi Bern (arXiv:1210.7709) eq. (1.1). It tells you that the theory is expected to be finite if $$D < 4 +\frac{6}{L}$$ for D-dimensions and L-number of loops. These come from looking at possible counter terms allowed by different symmetries and explicit calculations of different amplitudes. Introduction of the above paper should give you quite a good idea.