  We argue that N=4 supergravity is 3-loop UV finite because the relevant
supersymmetric candidate counterterm is known to be SL(2, R)x SO(6) invariant,
which violates the Noether-Gaillard-Zumino current conservation. Analogous
arguments, based on the universality properties of groups of type E7, also
apply to N=5,6,8 in 4,5,7 loops, respectively, since the 1/N BPS invariants
break duality symmetry between Bianchi identities and quantum corrected vector
field equations.
