Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking

Abstract

We present a renormalizable 4-dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which dynamically develops extra dimensions in the form of a fuzzy sphere S^2. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M^4 x S^2, the scalars being interpreted as gauge fields on S^2. The gauge group is broken dynamically, and the low-energy content of the model is determined. Depending on the parameters of the model the low-energy gauge group can be SU(n), or broken further to SU(n_1) x SU(n_2) x U(1), with mass scale determined by the size of the extra dimension.

27 pages. V2: discussion and references added, published version

References in corpus (17)

• (De)Constructing Dimensions
• Electroweak symmetry breaking and fermion masses from extra dimensions
• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• Noncommutative Geometry and Gauge Theory on Fuzzy Sphere
• The Origin of Spontaneous Symmetry Breaking in Theories with Large Extra Dimensions
• Scaling Limits of the Fuzzy Sphere at one Loop
• Spectrum of Schroedinger field in a noncommutative magnetic monopole
• Nonperturbative studies of fuzzy spheres in a matrix model with the Chern-Simons term
• Dimensional Reduction over Fuzzy Coset Spaces
• Deconstruction of the Maldacena-Nunez Compactification
• Spherical Deconstruction
• Dynamical generation of a nontrivial index on the fuzzy 2-sphere
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Perturbative dynamics of fuzzy spheres at large N
• Noncommutativity, Extra Dimensions, and Power Law Running in the Infrared
• Unified Theories from Fuzzy Extra Dimensions

Cited by in corpus (55)

• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Emergent Gravity from Noncommutative Gauge Theory
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Fermions on spontaneously generated spherical extra dimensions
• Intersecting branes and a standard model realization in matrix models
• Cosmological solutions of emergent noncommutative gravity
• Orbifolds, fuzzy spheres and chiral fermions
• Emergent Spacetime and The Origin of Gravity
• Emergent gravity on covariant quantum spaces in the IKKT model
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• Evidence for F(uzz) Theory
• Noncommutative gauge theory and symmetry breaking in matrix models
• Four-dimensional Gravity on a Covariant Noncommutative Space
• Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
• Equivariant reduction of Yang-Mills theory over the fuzzy sphere and the emergent vortices
• Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in $\mathcal{N}=4$ SYM and matrix models
• Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions
• On the 1-loop effective action for the IKKT model and non-commutative branes
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Lorentzian Fuzzy Spheres
• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
• Quantum (Matrix) Geometry and Quasi-Coherent States
• Schwarzschild Geometry Emerging from Matrix Models
• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• On Lie-algebraic solutions of the type IIB matrix model
• Localization for Yang-Mills Theory on the Fuzzy Sphere
• Noncommutative Gauge Theory and Gravity in Three Dimensions
• Curvature and Gravity Actions for Matrix Models
• Fermions on curved backgrounds of matrix models
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Black Hole Formation in Fuzzy Sphere Collapse
• Generalized Fuzzy Torus and its Modular Properties
• Probability distribution of the index in gauge theory on 2d non-commutative geometry
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Finite-matrix formulation of gauge theories on a non-commutative torus with twisted boundary conditions
• Index theorem in spontaneously symmetry-broken gauge theories on a fuzzy 2-sphere
• Probability of the Standard Model Appearance from a Matrix Model
• Dimensional reduction over the quantum sphere and non-abelian q-vortices
• Intertwining noncommutativity with gravity and particle physics
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Construction of a topological charge on fuzzy S^2 x S^2 via Ginsparg-Wilson relation
• Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• The instability of intersecting fuzzy spheres
• Dominance of a single topological sector in gauge theory on non-commutative geometry
• Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Zero point energy on extra dimension: Noncommutative Torus
• Gauge Symmetry Breaking in Matrix Models
• Heat kernel expansion and induced action for matrix models