Model Building by Coset Space Dimensional Reduction Scheme Using Ten-Dimensional Coset Spaces

Abstract

We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with a gauge theory in a fourteen-dimensional spacetime where extra-dimensional space has the structure of a ten-dimensional compact coset space. We found seventeen phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in fourteen dimension, and fermion representation. Of the seventeen, ten models led to SO(10)(×U (1)) GUT-like models after dimensional reduction, three models led to SU (5) × U (1) GUT-like models, and four toThe combinations of the coset space, the gauge group in the fourteen-dimensional spacetime, and the representation of the fermion contents of such models are listed. §1. IntroductionThe Standard Model (SM) has described the interactions of the elementary particles successfully. In this model, the Higgs scalar plays an essential role in the mechanism of spontaneous breaking of the gauge symmetry from SU (3) C ×SU (2) L ×U (1) Y down to SU (3) C × U (1) em , giving masses to the elementary particles. Nevertheless, the Higgs particle itself is still undiscovered. Not only is it the last frontier of the SM, it will also provide the key clue to the physics beyond the SM, since the SM does not address even the most fundamental nature of the Higgs particle, such as its mass and the self-coupling constants.The gauge-Higgs unification is one of attractive approaches to the physics beyond the SM in this regard 1)-3) (for recent approaches, see Refs. 4)-19)). In this approach, the Higgs sector is embraced into the gauge interactions in the spacetime with dimensions larger than four, where the extra-dimensional space is compactified to a small scale to reproduce the four-dimensional spacetime. The scalar particles originate from the extra-dimensional components of the gauge field and part of the fundamental properties of Higgs scalar is determined from the gauge interactions.We consider this approach in the framework of coset space dimensional reduction (CSDR) 20) (for recent approaches, see Refs. 21)-23)). This framework introduces a compact extra-dimensional space which has the structure of a coset of Lie groups, and identifies the gauge transformation as the translation within the extra-dimensional space. This identification determines both the gauge symmetry and the particle contents of the four-dimensional theory.

The Dark Sector and the Standard Model from a Local Generalisation of Extra Dimensions

“…This is in contrast with the long-standing programme of attempts to accommodate the elementary properties of visible matter through extra dimensions of space. These attempts date from the 5-dimensional spacetime theory of Kaluza one hundred years ago [52] to the modern-day quest to associate structures deriving from additional spatial dimensions over 4-dimensional spacetime with the matter fields of the Standard Model itself (see for example [53,54]). However, it has proven difficult to establish such a connection without the need for a somewhat contrived approach.…”

Octonions in Particle Physics through Structures of Generalised Proper Time

“…While providing a unifying geometrical framework, as initiated by Kaluza and Klein with the addition of a single extra dimension proposed to accommodate electromagnetism [26,27], extensions with further spatial dimensions in more modern theories have only achieved limited success in accounting for the Standard Model [28]. Indeed it has proved difficult even to accommodate the Standard Model within a suitably contrived structure of extra spatial dimensions (see for example [29]), with the goal of finding a unique and inevitable explanation for the properties of particle physics in this manner seemingly still somewhat remote.…”

Model building by coset space dimensional reduction in eight-dimensions

“…This approach counts the Higgs scalars as components of the gauge bosons in the spacetime with the dimension higher than four, and attributes their properties to the physical setups such as the gauge symmetry and the compactification scale of the extra-dimensional space. We consider this idea in the scheme of the coset space dimensional reduction, in which the extra-dimensional space is assumed to be a coset space of compact Lie groups, and the gauge transformation is identified as the translation within this space [1,21,22,23,24,25,26]. This identification determines both the gauge symmetry and the particle contents of the four-dimensional theory.…”