相关论文: Building SO$_{10}$- models with $\mathbb{D}_{4}$ s…

Representations of $\text{SO}(4,2)$ are constructed using $4\times4$ and $2\times2$ matrices with elements in $\mathbb{H}'\otimes\mathbb{C}$, and the known isomorphism between the conformal group and $\text{SO}(4,2)$ is written explicitly…

Standard SUSY-GUTs such as those based on $SU(5)$ or $SO(10)$ lead to predictions for the values of $\alpha _s$ and $sin^2\theta _W$ in amazing agreement with experiment. In this article we investigate how these models may be obtained from…

We provide a new tableau model from which one can easily deduce the characters of finite-dimensional irreducible polynomial representations of the special orthogonal group $SO_n(\mathbb{C})$. This model originates from the representation…

Let G be a semi-simple non-compact Lie group with unitary lowest/highest weight representations. We consider explicitly the relation between three types of representations of G: positive energy (unitary lowest weight)representations,…

Grand Unified Theories (GUTs) are a very well motivated extensions of the Standard Model (SM), but the landscape of models and possibilities is overwhelming, and different patterns can lead to rather distinct phenomenologies. In this work…

The complete tables of Clebsh-Gordan (CG) coefficients for a wide class of SO(10) SUSY grand unified theories (GUTs) are given. Explicit expression of all states and corresponding multiplets under standard model gauge group G_{321} =…

All possible permutations in the discrete $S_4$ group are classified by three rotation angles associated with the orthogonal group $O(3)$. We construct a spinor representation ${\bf 2}_D$ of $O(3)$, which is transformed by three 4$\times$4…

We study the breaking of a supersymmetric SO(10) GUT in 6 dimensions by orbifold compactification. In 4 dimensions we obtain a N=1 supersymmetric theory with the standard model gauge group enlarged by an additional U(1) symmetry. The…

We combine $SU(5)$ Grand Unified Theories (GUTs) with $A_4$ modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the…

Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type…

We present a new class of unified SO(10) models where the GUT symmetry breaking down to the standard model gauge group involves just one scale, in contrast to the conventional SO(10) models which require two scales. Further, the models we…

The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of…

We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and gauge group is a direct product of two Lie groups. We list up candidates of the gauge group and embeddings of $R$ into…

Let $n\le 5$ be an integer, and let $\Gamma$ be a finite group. We prove that if $\rho , \rho': \Gamma \to O(n)$ are two representations that are conjugate by an orientation-preserving diffeomorphism, then they are conjugate by an element…

We investigate gauge-Higgs unification models in eight-dimensional spacetime where extra-dimensional space has the structure of a four-dimensional compact coset space. The combinations of the coset space and the gauge group in the…

We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

We study the vacuum structure in 5D SO(10) grand unified theory (GUT) compactified on $S^1/Z_2$ orbifold, where SO(10) is broken into $SU(3)\times SU(2)\times U(1)^2$ through the boundary conditions. Although a lot of people extended to 6D…

A SUSY SO(10) $\times A_4$ GUT model is constructed for fermion masses and mixing by introducing a minimal set of low dimensional Higgs representations needed to break the guage symmetry down to $SU(3)_c \times U(1)_{em}$. The hierarchy of…

A unified description of spacetime and matter is proposed by using a single irreducible representation of SO(10) Super-Poincare algebra(SO(10)SPA). All (observed) elementary particles except the graviton are the (massless) eigenstates of…