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.
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