A survey of spectral models of gravity coupled to matter

Abstract

This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces. We present the important contributions that helped in the search and identification of the noncommutative space that characterizes the fine structure of space-time. The nature and properties of the noncommutative space are arrived at by independent routes and show the uniqueness of the Spectral Standard Model at low energies and the Pati-Salam unification model at high energies.

arXiv commentAn appendix is added to include scalar potential analysis for a Pati-Salam model. 58 Pages

References in corpus (49)

• 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
• Gravity and the standard model with neutrino mixing
• An Introduction to Noncommutative Spaces and their Geometry
• A Universal Action Formula
• Vacuum Stability, Perturbativity, and Scalar Singlet Dark Matter
• Gravity in Non-Commutative Geometry
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Why the Standard Model
• The Standard Model as a noncommutative geometry: the low energy regime
• Resilience of the Spectral Standard Model
• Classification of Finite Spectral Triples
• Fermion Hilbert Space and Fermion Doubling in the Noncommutative Geometry Approach to Gauge Theories
• 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
• Type III and spectral triples
• Quanta of Geometry: Noncommutative Aspects
• Almost-Commutative Geometries Beyond the Standard Model
• The standard model in noncommutative geometry and fermion doubling
• On a Classification of Irreducible Almost-Commutative Geometries IV
• The Gravitational Sector in the Connes-Lott Formulation of the Standard Model
• Grand Symmetry, Spectral Action, and the Higgs mass
• Geometry and the Quantum: Basics
• On a Classification of Irreducible Almost Commutative Geometries
• Grand Unification in the Spectral Pati-Salam Model
• Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra
• Lorentz signature and twisted spectral triples
• Non-Commutative Geometry, Non-Associative Geometry and the Standard Model of Particle Physics
• New Scalar Fields in Noncommutative Geometry
• Higgs mass in Noncommutative Geometry
• The Standard Model in noncommutative geometry: fundamental fermions as internal forms
• Supersymmetric QCD and noncommutative geometry
• A DETAILED ACCOUNT OF ALAIN CONNES' VERSION OF THE STANDARD MODEL IV
• Electrodynamics from Noncommutative Geometry
• The Standard Model as an extension of the noncommutative algebra of forms
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• On twisting real spectral triples by algebra automorphisms
• Connection between Space-Time Supersymmetry and Non-Commutative Geometry
• Gauge transformations for twisted spectral triples
• Almost-Commutative Geometries Beyond the Standard Model II: New Colours
• The Standard Model a la Connes-Lott
• A nonperturbative form of the spectral action principle in noncommutative geometry
• Spectral Action in Noncommutative Geometry
• Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model
• Clifford Structures in Noncommutative Geometry and the Extended Scalar Sector
• A Dark Sector Extension of the Almost-Commutative Standard Model
• Second Quantization and the Spectral Action
• Beyond the Standard Model: A Noncommutative Approach
• Clifford-based spectral action and renormalization group analysis of the gauge couplings

Cited by in corpus (14)

• Bootstrapping Dirac Ensembles
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• String Theory, the Dark Sector and the Hierarchy Problem
• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
• From Noncommutative Geometry to Random Matrix Theory
• Twisted Standard Model in noncommutative geometry I: the field content
• A $U(1{)}_{B-L}$-extension of the Standard Model from Noncommutative Geometry
• Lorentzian fermionic action by twisting euclidean spectral triples
• Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models
• From Quantum Foundations of Quantum Field Theory, String Theory and Quantum Gravity to Dark Matter and Dark Energy
• Connes Trace Theorem for Curved Noncommutative Tori. Application to Scalar Curvature
• Particle models from special Jordan backgrounds and spectral triples
• A critical survey of twisted spectral triples beyond the Standard Model
• Real Part of Twisted-by-Grading Spectral Triples