Unification of the four forces in the Spin(11,1) geometric algebra

Abstract

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 with $[N/2]$ bits. Fermions in Spin(10) are described by five bits $yzrgb$, consisting of two weak bits $y$ and $z$, and three colour bits $r$, $g$, $b$. If a sixth bit $t$ is added, necessary to accommodate a time dimension, then the enlarged Spin(11,1) algebra contains the standard-model and Dirac algebras as commuting subalgebras, unifying the four forces. The minimal symmetry breaking chain that breaks Spin(11,1) to the standard model is unique, proceeding via the Pati-Salam group. The minimal Higgs sector is similarly unique, consisting of the dimension~66 adjoint representation of Spin(11,1); in effect, the scalar Higgs sector matches the vector gauge sector. Although the unified algebra is that of Spin(11,1), the persistence of the electroweak Higgs field after grand symmetry breaking suggests that the gauge group before grand symmetry breaking is Spin(10,1), not the full group Spin(11,1). The running of coupling parameters predicts that the standard model should unify to the Pati-Salam group Spin(4)${}_w\times$Spin(6)${}_c$ at $10^{12}$GeV, and thence to Spin(10,1) at $10^{15}$GeV. The grand Higgs field breaks $t$-symmetry, can drive cosmological inflation, and generates a large Majorana mass for the right-handed neutrino by flipping its $t$-bit. The electroweak Higgs field breaks $y$-symmetry, and generates masses for fermions by flipping their $y$-bit.

52 pages, 3 figures. Accepted for publication in Physica Scripta

References in corpus (26)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Ultralight scalars as cosmological dark matter
• Leptogenesis
• Global status of neutrino oscillation parameters after Neutrino-2012
• Indications of Intermediate-Scale Anisotropy of Cosmic Rays with Energy Greater Than 57 EeV in the Northern Sky Measured with the Surface Detector of the Telescope Array Experiment
• Ultra Light Boson Dark Matter and Event Horizon Telescope Observations of M87*
• The Higgs Phenomenon in Quantum Gravity
• Leptogenesis in the Universe
• Different SO(10) Paths to Fermion Masses and Mixings
• Graviweak Unification
• Naturally Stable Right-Handed Neutrino Dark Matter
• Leptogenesis and fermion mass fit in a renormalizable $SO(10)$ model
• Leptogenesis in SO(10)
• A Predictive and Testable Unified Theory of Fermion Masses, Mixing and Leptogenesis
• Yukawa unification in SUSY SO(10) in light of the LHC Higgs data
• Division algebraic symmetry breaking
• A Predictive $SO(10)$ Model
• Spontaneous Symmetry Breaking as a Basis of Particle Mass
• SO(10): a Case for Hadron Colliders
• Spin(11,3), particles and octonions
• Quantum nature of the minimal potentially realistic $\mathrm{SO}(10)$ Higgs model
• All possible first signals of gauge leptoquark in quark-lepton unification and beyond
• SO(10) Grand Unification with Minimal Dark Matter and Color Octet Scalars
• An economical model for $B$-flavour and $a_{\mu }$ anomalies from SO(10) grand unification
• Geometry of Spin(10) Symmetry Breaking

Cited by in corpus (1)

• The Supergeometric Algebra