Why the Standard Model

Abstract

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 explanation: space-time has a fine structure given as a product of a four dimensional continuum by a finite noncommutative geometry F. The raison d'etre for F is to correct the K-theoretic dimension from four to ten (modulo eight). We classify the irreducible finite noncommutative geometries of K-theoretic dimension six and show that the dimension (per generation) is a square of an integer k. Under an additional hypothesis of quaternion linearity, the geometry which reproduces the Standard Model is singled out (and one gets k=4)with the correct quantum numbers for all fields. The spectral action applied to the product MxF delivers the full Standard Model,with neutrino mixing, coupled to gravity, and makes predictions(the number of generations is still an input).

13 pages

References in corpus (5)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Noncommutative Geometry and the standard model with neutrino mixing

Cited by in corpus (79)

• Resilience of the Spectral Standard Model
• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Life at the Interface of Particle Physics and String Theory
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification
• Inner Fluctuations in Noncommutative Geometry without the first order condition
• Quanta of Geometry: Noncommutative Aspects
• The Uncanny Precision of the Spectral Action
• Grand Symmetry, Spectral Action, and the Higgs mass
• Geometry and the Quantum: Basics
• Grand Unification in the Spectral Pati-Salam Model
• Particle Physics from Almost Commutative Spacetimes
• Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
• Lorentz signature and twisted spectral triples
• Matrix geometries and fuzzy spaces as finite spectral triples
• Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
• Higgs mass in Noncommutative Geometry
• Spectral Action for Robertson-Walker metrics
• Quantum Isometries of the finite noncommutative geometry of the Standard Model
• Supersymmetric QCD and noncommutative geometry
• A survey of spectral models of gravity coupled to matter
• Cyclic homology for Hom-associative algebras
• Product of real spectral triples
• $B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model
• Location and Direction Dependent Effects in Collider Physics from Noncommutativity
• Liberations and twists of real and complex spheres
• Early Universe models from Noncommutative Geometry
• Moduli spaces of Dirac operators for finite spectral triples
• The Spectral Action for Dirac Operators with skew-symmetric Torsion
• On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
• Noncommutative Geometry Spectral Action as a framework for unification: Introduction and phenomenological/cosmological consequences
• Noncommutative Geometric Spaces with Boundary: Spectral Action
• Understanding truncated non-commutative geometries through computer simulations
• Spectral Noncommutative Geometry, Standard Model and all that
• The graded product of real spectral triples
• Space-Time from the spectral point of view
• Noncommutativity and Physics: A non-technical review
• The geometry of physical observables
• On a Classification of Irreducible Almost-Commutative Geometries V
• Gravity assisted solution of the mass gap problem for pure Yang-Mills fields
• Quantum Holonomy Theory
• Noncommutative generalization of SU(n)-principal fiber bundles: a review
• Noncommutative Geometry as the Key to Unlock the Secrets of Space-Time
• Rationality of Spectral Action for Robertson-Walker Metrics
• Using an intense laser beam in interaction with muon/electron beam to probe the Noncommutative QED
• GUTs without guts
• Going beyond the Standard Model with noncommutative geometry
• Lifting spectral triples to noncommutative principal bundles
• A new algebraic structure in the standard model of particle physics
• A Dark Sector Extension of the Almost-Commutative Standard Model
• Spectral action in matrix form
• Clifford-based spectral action and renormalization group analysis of the gauge couplings
• Twisted Spectral Triples without the First-Order Condition
• On a Lattice-Independent Formulation of Quantum Holonomy Theory
• Supersymmetric Yang-Mills Theory on the Noncommutative Geometry
• Non-Associative Geometry and the Spectral Action Principle
• Quanta of Space-Time and Axiomatization of Physics
• Quanta of Geometry and Unification
• Quantum Holonomy Theory and Hilbert Space Representations
• Supersymmetry and noncommutative geometry Part I: Supersymmetric almost-commutative geometries
• Quantum Gravity and the Emergence of Matter
• Supersymmetry and noncommutative geometry Part III: The noncommutative supersymmetric Standard Model
• Supersymmetric QCD in the Noncommutative Geometry
• The superspace representation of Super Yang-Mills theory on NCG
• Implications of the complex Singlet field for Noncommutative Geometry model
• On the uniqueness of Barrett's solution to the fermion doubling problem in Noncommutative Geometry
• A critical survey of twisted spectral triples beyond the Standard Model
• Supersymmetry and the Spectral Action. On a geometrical interpretation of the MSSM
• Supergravity on the noncommutative geometry
• On the supersymmetric $N=1$ and $N=(1,1)$ spectral data : A multiplicativity property
• On gauge theories of mass
• Subadditivity and additivity of the Yang-Mills action functional in Noncommutative Geometry
• Noncommutative Geometry and Structure of Space-Time
• Origin of fermion generations from extended noncommutative geometry
• Gauge transformations of spectral triples with twisted real structures
• Real Part of Twisted-by-Grading Spectral Triples
• Projective real calculi over matrix algebras