Fermionic states in pure 4D deconstruction

Abstract

We study the structure of fermionic mass eigenstates in a pure four-dimensional deconstruction approach. Unlike the case with the usual higher dimensional deconstruction (or latticized extra dimension), here the doubling of fermionic degrees of freedom is physical, thus there is no need to invoke Wilson terms to eliminate them. The fermionic structure is shaped by two key factors, namely, the boundary conditions on fermions and the ratio of two breaking scales involved. The singular value decomposition of linear algebra is employed to shed light into the phenomenologically crucial role of chiral boundary conditions. In this approach, we can explain the localization or ``delocalization'' nature of fermionic zero-mode in flavor space and obtain analytically all higher modes. The application of boundary conditions on fermions to the implementation of CKM quark mixing is also found.