Intertwining noncommutativity with gravity and particle physics

Abstract

Here we present an overview on the various works, in which many collaborators have contributed, regarding the interesting dipole of noncommutativity and physics. In brief, we present the features that noncommutativity triggers both in the fields of gravity and particle physics, from a matrix-realized perspective, with the notion of noncommutative gauge theories to play the most central role in the whole picture. Also, under the framework of noncommutativity, we examine the possibility of unifying the two fields (gravity-particle physics) in a single configuration.

References in corpus (77)

• String Theory and Noncommutative Geometry
• M Theory As A Matrix Model: A Conjecture
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• A Large-N Reduced Model as Superstring
• 4d Conformal Field Theories and Strings on Orbifolds
• The Spectral Action Principle
• The Standard Model on Non-Commutative Space-Time
• Construction of non-Abelian gauge theories on noncommutative spaces
• Space-Time Structures from IIB Matrix Model
• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Deforming Einstein's Gravity
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• Noncommutative Standard Model: Model Building
• Nonabelian noncommutative gauge theory via noncommutative extra dimensions
• Non-Commutative GUTs, Standard Model and C,P,T
• The Standard Model as a noncommutative geometry: the low energy regime
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• The Z -> gamma gamma, gg Decays in the Noncommutative Standard Model
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• Emergent Gravity from Noncommutative Spacetime
• Describing Curved Spaces by Matrices
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Noncommutative D=4 gravity coupled to fermions
• An Invariant Action for Noncommutative Gravity in Four-Dimensions
• SL(2,C) Gravity with Complex Vierbein and Its Noncommutative Extension
• Finite Gauge Theory on Fuzzy CP^2
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Finite Unified Models
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• Dimensional Reduction over Fuzzy Coset Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^4 to all orders
• Covariant Non-Commutative Space-Time
• Chirality in unified theories of gravity
• Noncommutative Gravity in two Dimensions
• Three-dimensional Noncommutative Gravity
• On the ultraviolet behaviour of quantum fields over noncommutative manifolds
• Fermions on spontaneously generated spherical extra dimensions
• Scalar Field Theory on Fuzzy S^4
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
• Orbifolds, fuzzy spheres and chiral fermions
• Noncommutative supergravity in D=3 and D=4
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Gravity and the Structure of Noncommutative Algebras
• Covariant 4-dimensional fuzzy spheres, matrix models and higher spin
• Gravitational fields on a noncommutative space
• Noncommutative Einstein-AdS Gravity in three Dimensions
• Monte Carlo Simulation of a NC Gauge Theory on The Fuzzy Sphere
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Emergent gravity on covariant quantum spaces in the IKKT model
• The Energy-momentum of a Poisson structure
• Noncommutative gravity: fuzzy sphere and others
• Finite SU(N)^k Unification
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• Higgs Mass and Noncommutative Geometry
• Noncommutative Chern-Simons gauge and gravity theories and their geometric Seiberg-Witten map
• Reduction of Couplings and its application in Particle Physics
• Field Equations of Massless Fields in the New Interpretation of the Matrix Model
• On Unification of Gravity and Gauge Interactions
• Fuzzy de Sitter Space
• Four-dimensional Gravity on a Covariant Noncommutative Space
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• Supersymmetry Breaking by Dimensional Reduction over Coset Spaces
• Gravity on a fuzzy sphere
• Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model
• Unified Theories from Fuzzy Extra Dimensions
• WKB Approximation in Noncommutative Gravity
• Four-Dimensional Gravity on a Covariant Noncommutative Space (II)
• Finite Unification: Theory and Predictions
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$
• Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Cited by in corpus (3)

• Unification of Conformal and Fuzzy Gravities with Internal Interactions resulting in SO(10) and a Possible Probe through Stochastic Gravitational Wave Background
• $\hslash$-perturbative solutions of quantum Snyder and Yang models with parameters describing spontaneous symmetry breaking
• Unification of Gravities with GUTs