Classification and Dynamics of Equivalence Classes in SU(N) Gauge Theory on the Orbifold S1/Z2

The dynamical determination of the boundary conditions in SU(N) gauge theoryon the orbifold $S^1/Z_2$ is investigated. We classify the equivalence classesof the boundary conditions, and then the vacuum energy density of the theory ineach equivalence class is evaluated at one loop order. Unambiguous comparisonof the vacuum energy densities in the two theories in different equivalenceclasses becomes possible in supersymmetric theories. It is found that in thesupersymmetric SU(5) models with the Scherk-Schwarz supersymmetry breaking, thetheory with the boundary conditions yielding the standard model symmetry is inthe equivalence class with the lowest energy density, though the low energytheory is not identically the minimal supersymmetric standard model. We alsostudy how particular boundary conditions are chosen in the cosmologicalevolution of the universe.Comment: 29 pages. Numerical errors in the effective potential are correcte