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.

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

References in corpus (16)

• 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
• A Lorentzian version of the non-commutative geometry of the standard model of particle physics
• Why the Standard Model
• Resilience of the Spectral Standard Model
• Type III and spectral triples
• Quanta of Geometry: Noncommutative Aspects
• On a Classification of Irreducible Almost-Commutative Geometries IV
• Geometry and the Quantum: Basics
• Supersymmetric QCD and noncommutative geometry
• The Standard Model as an extension of the noncommutative algebra of forms
• Almost-Commutative Geometries Beyond the Standard Model II: New Colours
• Spectral Action in Noncommutative Geometry
• Beyond the Standard Model: A Noncommutative Approach
• Second Quantization and the Spectral Action
• 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