  We study N=2 supersymmetric gauge theories with $d=6$ bulk and $d=4$ brane
fields charged under a U(1) gauge symmetry. Radiatively induced
Fayet-Iliopoulos terms lead to an instability of the bulk fields. We compute
the profile of the bulk zero modes and observe the phenomenon of spontaneous
localization towards the position of the branes. While this mechanism is quite
similar to the $d=5$ case, the mass spectrum of the excited Kaluza-Klein modes
shows a crucial difference.
