7 Divergence Properties of Maximal Supergravity

In general, the larger the number of supersymmetries, the tamer the ultraviolet divergences because of the tendency for these to cancel between bosons and fermions in a supersymmetric theory. In four-dimensions maximal supergravity may therefore be expected to be the least divergent of all possible supergravity theories. Moreover, the maximally supersymmetric gauge theory, super-Yang–Mills, is completely finite [128, 98, 81], leading one to suspect that the superb ultraviolet properties of super-Yang–Mills would then feed into improved ultra-violet properties for supergravity via its relation to gauge theory. This makes the ultraviolet properties of supergravity the ideal case to investigate first via the perturbative relationship to gauge theory.