Fermion mass generation via Kaluza-Klein fermions under the influence of a gauge field within a (2 + 1)-dimensional model

We considered the generation of mass on a two-dimensional brane within a three-dimensional model with four-fermion interaction, including an external gauge field $A_3$. In the scope of this model, the generated mass proves to be lighter than the masses of the Kaluza-Klein modes. This indicates the possibility of solving the mass hierarchy problem in realistic four-dimensional models. As well, the dependences of the effective potential and the constant of coupling on such characteristics of the model as the radius of compactification, gauge field, and phase-shift parameter were obtained.