  We discuss the one-loop quantum corrections to the mass M and central charge
Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary
to previous expectations and published results, in each of these cases there
are nonvanishing quantum corrections to the mass. For the N=1 kink and the N=2
monopole a new anomaly in Z rescues BPS saturation (M=Z); for the N=2 vortex,
BPS saturation is rescued for two reasons: (i) the quantum fluctuations of the
Higgs field acquire a nontrivial phase due to the winding of the classical
solution, and (ii) a fermionic zero mode used in the literature is shown not to
be normalizable.
