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
N
=8 supergravity may therefore be expected to be the least
divergent of all possible supergravity theories. Moreover, the
maximally supersymmetric gauge theory,
N
=4 super-Yang-Mills, is completely finite [129,
97,
80], leading one to suspect that the superb ultraviolet properties
of
N
=4 super-Yang-Mills would then feed into improved ultra-violet
properties for
N
=8 supergravity via its relation to gauge theory. This makes the
ultraviolet properties of
N
=8 supergravity the ideal case to investigate first via the
perturbative relationship to gauge theory.