Related papers: Octonions, complex structures and Standard Model f…
This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…
The supersymmetric SO(10) GUT based on the ${\bf{210\oplus 10\oplus 120\oplus 126\oplus {\bar {126}}}}$ Higgs system provides a minimal framework for the emergence of the R-parity exact MSSM at low energies and a viable supersymmetric…
The Standard Model is based on the gauge invariance principle with gauge group U(1)xSU(2)xSU(3) and suitable representations for fermions and bosons, which are begging for a conceptual understanding. We propose a purely gravitational…
We develop the modification of the top - quark condensation scenario, in which the Higgs boson is composed of all Standard Model fermions. Within this scenario we suggest the phenomenological model with non - local four - fermion…
We explore unified field theories based on the gauge groups $SU(5)$ and $SO(10)$ using the worldline approach for chiral fermions with a Wilson loop coupling to a background gauge field. Representing path ordering and chiral projection…
A supersymmetric model with gauge symmetry G_1 X G_2, where G_i=SU(3)_i X SU(2)_i X U(1)_i, is constructed within the framework of gauge mediated supersymmetry breaking. At the energy scale (10-100) TeV where the gauge symmetry breaks down…
The conjecture of a hidden $E_{10}$ symmetry of M-theory is supported by the close connection between the dynamics of D=11 supergravity near a spacelike singularity and a truncation of an one-dimensional $\sigma$-model with $E_{10}$…
We show that in SO(10) models, a Yukawa sector consisting of a real $10_H$, a real $120_H$ and a complex $126_H$ of Higgs fields can provide a realistic fit to all fermion masses and mixings, including the neutrino sector. Although the…
It is noted that a set of facts points to the relevance in four dimensions of conventional supersymmetric unification based on minimally a string-unified G(224)-symmetry, or maximally SO(10). These include: (i) the observed family-…
We investigate Higgs Parity Unification-a realization of $SO(10)$ grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right…
The algebraic elements of gravitational and Standard Model gauge fields acting on a generation of fermions may be represented using real matrices. These elements match a subalgebra of spin(11,3) acting on a Majorana-Weyl spinor, consistent…
In accordance with known phenomenological facts on leptons and quarks in the Standard Model as well as on the scale of neutrino masses and introducing the supersymmetry, we logically substantiate the unique composition of fundamental…
An "expanded" description is introduced to examine the spinor-monopole identification proposed by Strassler for four-dimensional $\cal N$ = 1 supersymmetric Spin(10) gauge theories with matter in F vector and N spinor representations. It is…
The 8 $\times$ 8 matrix representation of SO(8) Symmetry has been defined by using the direct product of Pauli matrices and Gamma matrices. These 8 $\times$ 8 matrices are being used to describe the rotations in SO(8) symmetry. The…
Higgs multiplet in the vector-spinor representations of SO(10), i.e., the $144+\bar{144}$ multiplet can break the SO(10) gauge symmetry spontaneously in one step down to the Standard Model gauge group symmetry $SU(3)_C\times SU(2)_L\times…
The representation theory of the symmetric groups is intimately related to geometry, algebraic combinatorics, and Lie theory. The spin representation theory of the symmetric groups was originally developed by Schur. In these lecture notes,…
By constructing concrete complex-oriented maps we show that the eight-fold of the generator of the third integral cohomology of the spin groups Spin(7) and Spin(8) is in the image of the Thom morphism from complex cobordism to singular…
These lectures begin with a brief introduction to the minimal supersymmetric standard model (MSSM) and the various mechanisms for hidden sector supersymmetry breaking and go on to provide a pedagogical discussion of the various kinds of…
Grand Unified Theories based on the group SO(10) generically provide interesting and testable relations between the charged fermions and neutrino sector masses and mixings. In the light of the recent neutrino data, we reexamine these…
We propose an SO(10) grand unified theory which has the simplest Higgs structure discussed so far in the literature. We include only two Higgs scalars, a 210-plet and a 16-plet. In addition to the regular fermions we include one singlet,…