  We study new nonperturbative phenomena in N=1 heterotic string vacua
corresponding to pointlike bundle singularities in codimension three. These
degenerations result in new four-dimensional infrared physics characterized by
light solitonic states whose origin is explained in the dual F-theory model. We
also show that such phenomena appear generically in $E_7 \to E_6$ Higgsing and
describe in detail the corresponding bundle transition.
