Deconstruction of gauge symmetry breaking by discrete symmetry and G unification

We deconstruct the non-supersymmetric SU(5) breaking by discrete symmetry on the space-time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M^4\times S^1$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M^4\times S^1/(Z_2\times Z_2')$\end{document} in the Higgs mechanism deconstruction scenario. Also we explain the subtle point of how to exactly match the continuum results with the latticized results on the quotient space S1/Z2 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S^1/(Z_2\times Z_2')$\end{document}. We also propose an effective deconstruction scenario and discuss the gauge symmetry breaking by the discrete symmetry on the theory space in this approach. As an application, we suggest the GN unification where GN is broken down to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$SU(3)\times SU(2)\times U(1)^{n-3}$\end{document} by the bifundamental link fields and the doublet-triplet splitting can be achieved.