Related papers: A cosmotopological relation for a unified field th…
We discuss a grand unified theory (GUT) based on a $USp(32)$ GUT gauge group broken to its subgroups including a special subgroup. A GUT based on an $SO(32)$ GUT gauge group has been discussed on six-dimensional (6D) orbifold space…
We present two 3-family SU(5) grand unified models in the heterotic string theory. One model has 3 chiral families and 9 pairs of $5+{\overline 5}$ Higgs fields, and an asymptotically-free SU(2) X SU(2) hidden sector, where the two SU(2)s…
The clockwork mechanism, which can naturally explain the origin of small numbers, is implemented in $SO(10)$ grand unified theories to address the origin of hierarchies in fermion masses and mixings. We show that a minimal Yukawa sector…
We discuss an anthropic explanation of why there exist three generations of fermions. If one assumes that the right-handed neutrino sector is responsible for both the matter-antimatter asymmetry and the dark matter, then anthropic selection…
The success of SU(5)-like gauge coupling unification boundary conditions $g_3^2=g_2^2=5/3 g_1^2$ has biased most attempts to embed the SM interactions into a unified structure. After discussing the limitations of the orthodox approach, we…
We consider five dimensional (5D) supersymmetric SO(10) compactified on the orbifold $S^1/(Z_2\times Z_2')$ such that the SO(10) gauge symmetry is broken on both fixed points (branes), and the residual gauge symmetry is $SU(3)_c\times…
I review the unification of gauge couplings of strong, weak and electro-magnetic interactions. I start by recalling the history of the most important prediction of low-energy supersymmetry: the correct value of the weak mixing angle tied to…
Motivated by experimental measurements indicating deviations from the Standard Model predictions we discuss F-theory inspired models, which, in addition to the three chiral generations contain a vector-like complete fermion family. The…
We construct the SU(5) and SO(10) models from F-theory. Turning on the U(1) fluxes, we can break the SU(5) gauge symmetry down to the Standard Model (SM) gauge symmetry, and break the SO(10) gauge symmetry down to the SU(3)_C X SU(2)_L X…
A new mechanism is proposed to explain the appearance of the three known fermion generations in a natural way. The underlying idea is based on the discreteness of the spectrum of solutions of the gap equation appearing in models of…
We propose the $SU(3)_C\times SU(3)_L\times U(1)_X$ model arising from $SU(6)$ breaking. One family of the Standard Model (SM) fermions arises from two $\bar{6}$ representations and one $15$ representation of $SU(6)$ gauge symmetry. To…
The models with the gauge group $SU(3)_c\times SU(3)_L \times U(1)_X$ (331-models) have been advocated to explain why there are three fermion generations in Nature. As such they can provide partial understanding of the flavour sector. The…
With the advent of neutrino masses, it has become more and more acknowledged that SO(10) is a more suitable theory than SU(5): it leads naturally to small neutrino masses via the see-saw mechanism, it has a simpler and more predictive…
We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of…
A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r+1/2, is inconsistent. We…
Grand Unified Theories (GUTs) based on groups like $SO(10)$ and $SU(5)$ unify Standard Model (SM) fermions into irreducible representations (irreps), and predict additional scalar fields beyond the SM Higgs. In $SO(10)$ GUTs, the scalar…
We analyze a gauge-Higgs unification model which is based on a gauge theory defined on a six-dimensional spacetime with an $S^2$ extra-space. We impose a symmetry condition for a gauge field and non-trivial boundary conditions of the $S^2$.…
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…
The properties of the one-dimensional $SU(3)$ population-imbalanced fermions are discussed. The system is assumed to be in the two-body resonance where all two-body scattering lengths diverge, and the only interaction between fermions that…
We initiate the study of the effects of strongly-coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time reversal…