Effective gauge theories on domain walls via bulk confinement?

We study with lattice techniques the localisation of gauge fields on domain wall defects in 2+1 dimensions, following a scenario originally proposed by Dvali and Shifman for 3+1 dimensions, based on confining dynamics in the bulk. We find that a localised gauge zero-mode does exist, if the domain wall is wide enough compared with the confinement scale in the bulk. The range of applicability of the corresponding low-energy effective theory is determined by the mass gap to the higher modes. For a wide domain wall, this mass gap is set by ``Kaluza--Klein modes'' as determined by the width. It is pointed out that in this regime the dynamical energy scales generated by the interactions of the localised zero-modes are in fact higher than the mass gap. Therefore, at least in 2+1 dimensions, the zero-modes alone do not form a low-energy effective gauge theory of a traditional type. Finally, we discuss how the situation is expected to change in going to 3+1 dimensions.