Related papers: An Algebraic Roadmap of Particle Theories, Part II…
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric…
We reconsider the issue of spontaneous symmetry breaking in SO(10) grand unified theories. The emphasis is put on the quest for the minimal Higgs sector leading to a phenomenologically viable breaking to the standard model gauge group.…
Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) $\mapsto$…
In the context of supersymmetric $SO(10)$ grand unified models, it is shown that the gauge symmetry breaking as well as a natural doublet--triplet splitting can be achieved with a minimal Higgs system consisting of a single adjoint and a…
A new SO(10) unified model is proposed based on a one step breaking of SO(10) to the Standard Model gauge group $SU(3)\times SU(2)\times U(1)_Y$ using a single 144 of Higgs. The symmetry breaking occurs when the SU(5) 24-plet component of…
SO(10), or equivalently its covering group Spin(10), is a well-known promising grand unified group that contains the standard-model group. The spinors of the group Spin($N$) of rotations in $N$ spacetime dimensions are indexed by a bitcode…
We construct supersymmetric models of SO(10) unification in which the gauge symmetry is broken by orbifold compactification. We find that using boundary conditions to break the gauge symmetry down to $SU(3)_C \otimes SU(2)_L \otimes U(1)_Y…
We embed the flipped SU(5) models into the SO(10) models. After the SO(10) gauge symmetry is broken down to the flipped SU(5) \times U(1)_X gauge symmetry, we can split the five/one-plets and ten-plets in the spinor \mathbf{16} and…
Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a…
Despite the successes of the Standard Model of particle physics, it is known to suffer from a number of deficiencies. Several of these can be addressed within non-supersymmetric theories of grand unification based on $\mathrm{SO}(10)$.…
What symmetry breaking would be required for gauginos from a supersymmetric theory to behave like left-handed quarks of the Standard Model? Starting with a supersymmetric SU(3)xSU(3)xU(1)xU(1) gauge theory, the 18 adjoint-representation…
We consider SUSY SO(10) models in which SUSY breaking occurs via an F-term which does not transform as an SO(10) singlet. This results in non-universal GUT-scale gaugino masses leading to a different pattern of sparticle masses from what is…
We consider supersymmetric SO(10) grand unification where the unified gauge group can break to the Standard Model gauge group through different chains. The breaking of SO(10) necessarily involves the reduction of the rank, and consequent…
I review some recent results on the Higgs sector of minimal SO(10) grand unified theories both with and without supersymmetry. It is shown that nonsupersymmetric SO(10) with just one adjoint triggering the first stage of the symmetry…
We explore the phenomenology of supersymmetric SO(10) grand unified theories with gauge mediated supersymmetry breaking. We show that if SO(10) breaking proceeds through intermediate left-right symmetric gauge groups which are broken at the…
We study a class of nonsupersymmetric SO(10) grand unified scenarios where the first stage of the symmetry breaking is driven by the vacuum expectation values of the 45-dimensional adjoint representation. Three decade old results claim that…
We continue our study of Coleman-Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the $SU(8)$ model we proposed earlier. We focus in this paper on qualitative features that will determine…
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…