Low-energy effective theory from a non-trivial scalar background in   extra dimensions
  Consequences of a non-trivial scalar field background for an effective 4D theory were studied in the context of one compact extra dimension. The periodic background that appears within the (1+4)-dimensional $\phi^4$ theory was found and the excitations above the background (and their spectrum) were determined analytically. It was shown that the presence of the non-trivial solution leads to the existence of a minimal size of the extra dimension that is determined by the mass parameter of the scalar potential. It was proved that imposing orbifold antisymmetry boundary conditions allows us to eliminate a negative mass squared Kaluza-Klein ground-state mode that otherwise would cause an instability of the system. The localization of fermionic modes in the presence of the non-trivial background was discussed in great detail varying the size of the extra dimension and the strength of the Yukawa coupling. A simple exact solution for the zero-mode fermionic states was found and the solution for non-zero modes in terms of trigonometric series was constructed. The fermionic mass spectrum, which reveals a very interesting structure, was found numerically. It was shown that the natural size of the extra dimension is twice as large as the period of the scalar background solution. 
Bohdan Grzadkowski (Warsaw U. and CERN), Manuel Toharia (UC, Davis)