We construct brane solutions in 6-dimensional Einstein-Skyrme systems. A class of baby skyrmion solutions realizes warped compactification of the extra dimensions and gravity localization on the brane for negative bulk cosmological constant. Coupling of the fermions with the brane skyrmions lead to the brane localized fermions. In terms of the level crossing picture, emergence of the massive localized modes are observed. Nonlinear nature of the skyrmions brings richer information for the fermions level structure. It comprises doubly degenerate lowest plus single excited modes. The three generation of the fundamental fermions is associated with this distinctive structure. The mass hierarchy of quarks or leptons is appeared in terms of a slightly deformed baby-skyrmions with topological charge three.

We shall consider about a 3-brane embedded in six-dimensional space-time with a negative bulk cosmological constant. The 3-brane is constructed by a topological soliton solution living in two-dimensional axially symmetric transverse subspace. Similar to most previous works of sixdimensional soliton models, our Maxwell gauged CP 1 brane model can also achieve to localize gravity around the 3-brane. The CP 1 field is described by a scalar doublet and derived from O(3) sigma model by projecting it onto two-dimensional complex space. In that sense, our framework is more effective than other solitonic brane models concerning with gauge theory. We shall also discuss about linear stability analysis for our new model by fluctuating all fields.

We construct two distinct brane solutions in six dimensional effective field theory models. The CP 1 sigma model and the baby skyrmion realize warped compactification of the extra dimensions for negative bulk cosmological constant. Higher winding number solutions of the baby skyrmion are also presented.

We investigate a fermionic O(3) σ model in 2+1 dimensions, taking into account the valence and the Casimir energies. The model exhibits the soliton solutions with various winding numbers. Lagrangian, which we used above, is extended into 6 dimensional brane world scenario and the fermion localization problem. In terms of the level crossing picture, emergence of the massive localized modes as well as the zero mode are found.