Special grand unification

Abstract

We discuss new-type grand unified theories based on grand unified groups broken to their special subgroups as well as their regular subgroups. In the framework, when we construct four-dimensional (4D) chiral gauge theories, i.e., the Standard Model (SM), 4D gauge anomaly cancellation restricts the minimal number of generations of the 4D SM Weyl fermions. We show that in a six-dimensional (6D) SU (16) gauge theory on M 4 × T 2 /Z 2 one generation of the SM fermions can be embedded into a 6D bulk Weyl fermion. For the model including three chiral generations of the SM fermions, the 6D and 4D gauge anomalies on the bulk and fixed points are canceled out without exotic 4D chiral fermions. * Electronic address: yamatsu@cc.kyoto-su.ac.jp

String-inspired special grand unification

“…First, we consider the pure SU (16) gauge anomaly cancellation. The 4D SU (16) gauge anomaly of twelve 4D SU (16) 16 left-handed Weyl fermions is canceled out by the anomaly of a 4D SU (16) 120 Weyl fermion [23]. (It can be checked by using 4D SU (16) anomaly coefficients listed in Ref.…”

“…Recently, a new-type GUT has been proposed by the author in Ref. [23]. In usual GUTs, GUT gauge groups are broken to their regular subgroups; e.g., E 6 ⊃ SO(10) × U (1) ⊃ SU (5) × U (1) × U (1) ⊃ G SM × U (1) × U (1).…”

Dynamical breaking to special or regular subgroups in the SO(N) Nambu–Jona-Lasinio model

“…Thus, the pair condensation of the 4 (4) spinor fermion cannot realize the global minimum of the potential. This argument actually holds for all cases of odd n = 2ℓ + 1, for which the chiral spinor is complex 41) and the symmetric product of SO(2n) = SO(4ℓ + 2) spinor contains the SU (n) singlet only in the R 0 (rank n tensor). The mass operator M n is thus given by M n = ma † 1 a † 2 · · · a † n or ma n a n−1 · · · a 2 a 1 .…”

Family unification in special grand unification

“…As in Refs. [50,51], an SU (19) special GUT on 6D orbifold spacetime M 4 × T 2 /Z 2 with the Randall-Sundrum (RS) type metric [31,32,53] given by…”

“…An SU (16) 5440 contains singlet under its SO(10) special subgroup. Its nonvanishing VEV can break SU (16) to its special subgroup SO(10) [50,51], where their SO(10) decompositions are given in Ref. [34] by (10)) ⊃ SU (5) to G SM , where its branching rule of…”