Abstract
We revisit the residual symmetries that survive the orbifold projections, and find additional transformations that have been overlooked in the past. Some of these transformations are outer automorphisms of the downstairs continuous symmetry group. Examples for these transformations include the left-right parity of the Pati-Salam model and its left-right symmetric subgroup.
Highlights
Gauge symmetry breaking via orbifolding [1,2,3] is a popular alternative to spontaneous breakdown of gauge symmetry in four dimensions
III we revisit the conditions for residual symmetries and shall show that in the past some symmetries were missed
2Note that “≃” means “up to Z2 factors,” but these Z2’s are different from the one we are going to discuss. This simple orbifold grand unified theory (GUT) gives rise to the well-known leftright parity [15], where it originates from SO(10) and is clearly a discrete gauge symmetry
Summary
Gauge symmetry breaking via orbifolding [1,2,3] is a popular alternative to spontaneous breakdown of gauge symmetry in four dimensions. The main purpose of this paper is to point out that there are additional discrete symmetries that have not been identified, or discussed, in this context far. III we revisit the conditions for residual symmetries and shall show that in the past some symmetries were missed We present two examples which could be of relevance for flavor model building from orbifold GUTs. Sec. V contains our summary.
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