相关论文: Three Generations and a Trio of Trialities

We obtain a three generational $SU(3)_c\times SU(3)_w \times U(1)^4\times [SO(12)\times U(1)^2]^\prime$ model from an orbifold construction with the requirement that three generations arise from twisted sectors. There exist supersymmetric…

A considerable amount of the standard model's three-generation structure can be realised from just the $8\hspace{.3mm}\mathbb{C}$-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can…

Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of $SU(3)$, $SU(2)$, and $SU(3)…

The extension of the Standard Model to $SU(3)_L \times SU(3)_R \times SU(3)_C$ (the trinification group) augmented by the $ SO(3)_G $ flavor group is considered. In our phenomenological treatment partly known and partly proposed vacuum…

We point out a somewhat mysterious appearance of $SU_c(3)$ representations, which exhibit the behaviour of three full generations of standard model particles. These representations are found in the Clifford algebra $\mathbb{C}l(6)$, arising…

The property of triality only appears in one linear simple Lie algebra: $D_4$, a.k.a. $\mathfrak{so}(8, \mathbb{C})$. Though often explored in abstract, it is desirable to have an explicit realization of the concept since there are no other…

We analyze the extension of the Minimal Supersymmetric Standard Model which includes extra Y=(0,\pm 1) supersymmetric triplets with a global SU(2)_L \otimes SU(2)_R symmetry spontaneousy broken to the custodial SU(2)_V by the vacuum…

We all know that in our family of particle physics we have three generations but still don't know why - the so-called "family problem". On other hand, in view of the masses and oscillations, the neutrinos now present some basic difficulty…

We present an extension of the Standard Model that results from the dimensional reduction of the $\mathcal{N}=1$, $10D$ $E_8$ group over a $M_4 \times B_0/ \mathbf{Z}_3 $ space, where $B_0$ is the nearly-K\"ahler manifold $SU(3)/U(1) \times…

Results are obtained on extending flat vector bundles or equivalently general representations from the fundamental group of S, a connected subsurface of the connected boundary of a compact, connected, oriented 3-dimensional manifold, to the…

In this letter, we introduce a new approach to formulate the family structure of the standard model. Trying to mimic the highly contrained representation structure of the standard model while extending the symmetry, we propose a…

The coupling coefficients (3j-symbols) for the symmetric (most degenerate) irreducible representations of the orthogonal groups SO(n) in a canonical basis and different semicanonical (tree) bases [with SO(n) restricted to SO(n')\times…

6D spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations…

We investigate all spherically symmetric fundamental monopole solutions with fixed topological charge in the SU(5) --> SU(3)xSU(2)xU(1)/Z_3xZ_2 symmetry breaking. We find that there is three-fold replication of the monopoles. The three…

We present a supersymmetric (SUSY) model based on trinification $[\mathrm{SU}(3)]^3$ and family $\mathrm{SU}(3)_\mathrm{F}$ symmetries embedded into a maximal subgroup of $\mathrm{E}_8$, where the sectors of light Higgs bosons and leptons…

We discuss how the Standard Model particles appear from the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory,…

We develop simple computational techniques for constructing all possible SU(3) representations in terms of irreducible SU(3) Schwinger bosons. We show that these irreducible Schwinger oscillators make SU(3) representation theory as simple…

We resolve the SU(3) outer multiplicity problem by defining all possible $SU(3)\otimes SU(3)$ invariant operators in terms of SU(3) Schwinger bosons. We show that the elementary invariant operators relevant to the outer multiplicity problem…

Motivated by physical and topological applications, we study representations of the group $\mathcal{LB}_3$ of motions of $3$ unlinked oriented circles in $\mathbb{R}^3$. Our point of view is to regard the three strand braid group…

We propose an interpretation for the adjoint representation of the $SO(32)$ group to classify the scalars of a generic Supersymmetric Standard Model having just three generations of particles, via a flavour group $SU(5)$. We show that this…