  We present a novel mechanism for generating gauge-invariant fermion masses
through global anomalies at the three loop level. In a gauge theory, global
anomalies are triggered by the possible existence of scalar or pseudoscalar
states and heavy fermions, whose masses may not necessarily result from
spontaneous symmetry breaking. The implications of this mass-generating
mechanism for model building are discussed, including the possibility of
creating low-scale fermion masses by quantum gravity effects.
