Non-Abelian gauge field localization on walls and geometric Higgs mechanism

Combining the semiclassical localization mechanism for gauge fields with $N$ domain wall background in a simple $\text{SU}(N)$ gauge theory in 5 space-time dimensions, we investigate the geometric Higgs mechanism, where a spontaneous breakdown of the gauge symmetry comes from splitting of domain walls. The mass spectra are investigated in detail for the phenomenologically interesting case $\text{SU}(5) \to \text{SU}(3)\times \text{SU}(2)\times \text{U}(1)$ , which is realized on a split configuration of coincident triplet and doublet of domain walls. We derive a low-energy effective theory in a generic background using the moduli approximation, where all nonlinear interactions between effective fields are captured up to 2 derivatives. We observe novel similarities between domain walls in our model and D-branes in superstring theories.