A supersymmetric grand unified model with noncompact horizontal symmetry

Abstract

In a supersymmetric SU (5) grand unified model with a horizontal symmetry SU (1, 1), we discuss spontaneous generation of generations to produce three chiral generations of quarks and leptons and one generation of higgses by using one structure field with a half-integer spin of SU (1, 1) and two structure fields with integer spins. In particular, the colored higgses can disappear without fine-tuning. The difference of the Yukawa coupling matrices between the down-type quarks and charged leptons is discussed. We show that some special SU (1, 1) weight assignments include R-parity as a discrete subgroup, and R-parity remains even after we take into account the SU (1, 1) breaking effects from all the VEVs of the structure and matter fields. The assignments forbid the baryon and/or lepton number violating terms except a superpotential quartic term including a coupling of two lepton doublets and two up-type higgses. We discuss how to generate sizable neutrino masses. We show that the proton decay derived from the colored higgses is highly suppressed.

Family unification in special grand unification

“…We have discussed how to embed three chiral generations of quarks and leptons in triplet (a finite-dimensional representation) of a non-Abelian compact group SU (3) F . Another direction for unifying generations may be considered by using non-Abelian noncompact groups (e.g., SU (1, 1)) and their infinite-dimensional representation [5,[62][63][64][65][66][67][68].…”

Four interactions in the sedenion curved spaces

“…For the purpose of containing the gravitational field, certain scholars advanced several new theoretical assumptions [7,8,9], including the Grand Unified Theory [10,11], 'Beyond the SM' [12,13], superstring theory [14,15], and 'Beyond the General Relativity' and so forth [16,17]. Although it may be encountered a large number of difficulties, these ambitious theoretical assumptions [18,19] do offer promising hope for the future to unify the existing four fields. By means of these ambitious plans, scholars expect the researches to be able to resolve some remaining problems [20,21] in the existing field theories, especially the field equations of the four fields [22,23,24], which are relevant to the classical mechanics and quantum mechanics, in the curved spaces.…”

Gauge coupling unification in gauge–Higgs grand unification

“…The Standard Model (SM) is based on gauge symmetry G SM := SU (3) C ×SU (2) L × U (1) Y in four-dimensional (4D) spacetime with the spontaneous electroweak (EW) symmetry breaking G SM to SU (3) C × U (1) em via the nonvanishing vacuum expectation value (VEV) of the SM Higgs boson. To construct a unified theory beyond the SM, here we use two notions; gauge-Higgs unification [1][2][3][4][5] and grand unification [6][7][8][9][10][11][12][13][14][15][16][17][18]. Gauge-Higgs unification is based on gauge symmetry in higher-dimensional spacetime.…”