Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

Abstract

The purpose of this letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the Standard Model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducibe geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the Standard Model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input. The geometrical model is valid at the unification scale, and has relations connecting the gauge couplings to each other and to the Higgs coupling. This gives a prediction of the Higgs mass of around 170 GeV and a mass relation connecting the sum of the square of the masses of the fermions to the W mass square, which enables us to predict the top quark mass compatible with the measured experimental value. We thus manage to have the advantages of both SO(10) and Kaluza-Klein unification, without paying the price of plethora of Higgs fields or the infinite tower of states.

arXiv commentTitle change only. The title "A Dress for SM the Beggar" was changed by the Editor of Physical Review Letters

References in corpus (7)

• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• A Universal Action Formula
• Matching conditions and Higgs mass upper bounds revisited
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Noncommutative Geometry and the standard model with neutrino mixing
• Why the Standard Model

Cited by in corpus (55)

• Topics in Noncommutative Geometry Inspired Physics
• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification
• Probing Models of Extended Gravity using Gravity Probe B and LARES experiments
• Cosmology and the Noncommutative approach to the Standard Model
• The Uncanny Precision of the Spectral Action
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Grand Symmetry, Spectral Action, and the Higgs mass
• Natural inflation mechanism in asymptotic noncommutative geometry
• Gravitational Waves in the Spectral Action of Noncommutative Geometry
• Noncommutativity and Non-anticommutativity in Perturbative Quantum Gravity
• Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
• Constraints on NonCommutative Spectral Action from Gravity Probe B and Torsion Balance Experiments
• Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
• Noncommutative spectral geometry, algebra doubling and the seeds of quantization
• Spectral Action for Robertson-Walker metrics
• Supersymmetric QCD and noncommutative geometry
• Cyclic homology for Hom-associative algebras
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Spectral dimensions from the spectral action
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• The Spectral Action for Dirac Operators with skew-symmetric Torsion
• Moduli spaces of Dirac operators for finite spectral triples
• Noncommutative Geometry Spectral Action as a framework for unification: Introduction and phenomenological/cosmological consequences
• Non-compact spectral triples with finite volume
• Noncommutative Geometric Spaces with Boundary: Spectral Action
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• The graded product of real spectral triples
• Spectral Noncommutative Geometry, Standard Model and all that
• Heat Trace Asymptotics on Noncommutative Spaces
• Holographic quark gluon plasma with flavor
• Space-Time from the spectral point of view
• Thermodynamics on Fuzzy Spacetime
• On a Classification of Irreducible Almost-Commutative Geometries V
• Intertwining noncommutativity with gravity and particle physics
• Rationality of Spectral Action for Robertson-Walker Metrics
• Noncommutative Geometry as the Key to Unlock the Secrets of Space-Time
• Quantum Gravity and Cosmology: an intimate interplay
• Noncommutative spectral geometry, dissipation and the origin of quantization
• Doubling of the Algebra and Neutrino Mixing within Noncommutative Spectral Geometry
• A new algebraic structure in the standard model of particle physics
• Noncommutative Spectral Geometry: A Short Review
• Supersymmetric Yang-Mills Theory on the Noncommutative Geometry
• Supersymmetric Dirac Operator on the Noncommutative Geometry
• Cosmological consequences of the noncommutative spectral geometry as an approach to unification
• Non-Associative Geometry and the Spectral Action Principle
• Aspects of the Bosonic Spectral Action
• Noncommutative Gauge Theories and Gravity
• Supersymmetric QCD in the Noncommutative Geometry
• The superspace representation of Super Yang-Mills theory on NCG
• Non-commutativity in Unified Theories and Gravity
• Origin of fermion generations from extended noncommutative geometry
• Real Part of Twisted-by-Grading Spectral Triples
• Supergravity on the noncommutative geometry
• Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory