Effective (2+1)-dimensional field theory of fermions: fermion mass generation with Kaluza-Klein fermions and gauge field

Generation of mass on two-dimensional brane in three-dimensional model with four-fermion interaction including external gauge field A3 is considered. In the framework of this model the generated mass proves to be lighter than Kaluza-Klein modes, thus indicating to a possibility of solving the mass hierarchy problem. Dependence of the effective potential and the coupling constant on characteristics of the model such as compactification radius, gauge field and phase shift parameter was also obtained. It is demonstrated that the generated mass, besides the dynamic part, includes also a kinematic (topological) contribution, i.e. the Aharonov-Bohm phase.