Related papers: Three Generations on the Quintic Quotient
We give an alternative description of the Schoen manifold as the blow-up of a Z2xZ2 orbifold in which one Z2 factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded,…
By the results of the author and Chiantini in Math.AG/0110102, on a general quintic threefold $X \subset {\mathbf P}^4$ the minimum integer $p$ for which there exists a positive dimensional family of irreducible rank $p$ vector bundles on…
The perfect fit of the matter fields of the Standard Model (SM) into the $SU(5)$ multiplets has strongly supported the idea of the Grand Unified Theory (GUT) for decades. In this paper, we discuss a novel framework which explains why the SM…
Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge…
In this paper we continue our study of the moduli space of stable bundles of rank two and degree 1 on a very general quintic surface. The goal in this paper is to understand the irreducible components of the moduli space in the first case…
We discuss family unification in grand unified theory (GUT) based on an $SU(19)$ GUT gauge group broken to its subgroups including a special subgroup. In the $SU(19)$ GUT on the six-dimensional (6D) orbifold space $M^4\times…
We propose a supersymmetric (SUSY) SU(5) Grand Unified Theory (GUT) including a single right-handed neutrino singlet and an adjoint matter representation below the GUT scale and extend this model to include an A4 family symmetry and a…
We classify $G$-Mori fibre spaces equivariantly birational to smooth quadric threefolds with fixed-point free actions of the alternating group $G=\mathfrak A_5$. We deduce that such quadric threefolds are $G$-solid and the $G$-actions on…
A three-generation Pati-Salam model is constructed by compactifying the heterotic string on a particular T^6/Z_6 Abelian symmetric orbifold with two discrete Wilson lines. The compactified space is taken to be the Lie algebra lattice…
A Z_2 orbifold compactification of the heterotic string is considered. The resulting 6D GUT groups can be SO(16) or E_7 times SU(2) plus some hidden sector groups. The N=4 supersymmetry is reduced to N=2. In particular, the SO(16) 6D model…
In this talk I discuss the problems and virtues of SUSY GUTs in four dimensions. I then show how to solve some of these problems, without foregoing the virtues, by considering an SO(10) SUSY GUT in five dimensions. I discuss gauge coupling…
With the apparent discovery of the Higgs boson, the Standard Model has been confirmed as the theory accounting for all sub-atomic phenomena. This observation lends further credence to the perturbative unification in Grand Unified Theories…
We construct new supersymmetric SU(5) Grand Unified Models based on Z4 x Z2 orientifolds with intersecting D6-branes. Unlike constructions based on Z2 x Z2 orientifolds, the orbifold images of the three-cycles wrapped by D6-branes…
We consider 5 dimensional E_6 and E_7 supersymmetric grand unified theories (GUTs) on an orbifold S^1/Z_2, in which the Higgs fields arise from the 5th components of the 5D gauge fields. We introduce matter fields in 5 dimensions, then the…
The instability of protons is a crucial prediction of supersymmetric GUTs. We review the decay in minimal supersymmetric SU(5), which is dominated by dimension-five operators, and discuss the implications of the failure of Yukawa…
Non-flat fibrations often appear in F-theory GUT models, and their interpretation is still somewhat mysterious. In this note we explore this issue in a model of particular phenomenological interest, the global $SU(5)\times U(1)$…
We study the generation of the GUT scale through radiative corrections in the context of a R-symmetric "flipped" SU(5) X U(1)_X model. A negative mass squared term for the GUT Higgs fields develops due to radiative effects along a flat…
We construct a novel invariant of braids and knots, secant-quandle (SQ),with generic secants serving as generators and generic horizontal trisecants serving as relations, i.e., $SQ = \Gamma \left< \mathcal{S}_M\mid…
For supersymmetric GUT models from heterotic string theory, built from a stable holomorphic SU(n) vector bundle $V$ on a Calabi-Yau threefold $X$, the net amount of chiral matter can be computed by a Chern class computation. Corresponding…
The trinification grand unified theory (GUT) has gauge group SU(3)^3 and a discrete symmetry permuting the SU(3) factors. In common with other GUTs, the attractive nature of the fermionic multiplet assignments is obviated by the complicated…