Codimension-Three Bundle Singularities in F-Theory

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.