The Standard Model Gauge Symmetry from Higher-Rank Unified Groups in Grand Gauge-Higgs Unification Models

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and $E_6$ models. In each model, the rank of the residual gauge symmetry that respects the boundary condition imposed at the orbifold fixed points is higher than that of the standard model. We verify that the residual symmetry is broken to the standard model gauge symmetry at the global minima of the effective potential for certain sets of bulk fermion fields in each model.Comment: 34 pages, 1 figure, clarifications added in Sec. 6, published versio

Model Building of Metal Oxide Surfaces and Vibronic Coupling Density as a Reactivity Index: Regioselectivity of CO2_2 Adsorption on Ag-loaded Ga2_2O3_3

The step-by-step hydrogen-terminated (SSHT) model is proposed as a model for the surfaces of metal oxides. Using this model, it is found that the vibronic coupling density (VCD) can be employed as a reactivity index for surface reactions. As an example, the regioselectivity of CO$_2$ adsorption on the Ag-loaded Ga$_2$O$_3$ photocatalyst surface is investigated based on VCD analysis. The cluster model constructed by the SSHT approach reasonably reflects the electronic structures of the Ga$_2$O$_3$ surface. The geometry of CO$_2$ adsorbed on the Ag-loaded Ga$_2$O$_3$ cluster has a bent structure, which is favorable for its photocatalytic reduction to CO.Comment: 18 pages, 11 figure