Dimensional Reduction over Fuzzy Coset Spaces

Abstract

We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.

Latex, 23 pages, 1 reference added, 1 reference updated. Final version, improved presentation and organization of the paper, in particular Section 3.1

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Cited by in corpus (42)

• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Finite Gauge Theory on Fuzzy CP^2
• Dynamical generation of fuzzy extra dimensions, dimensional reduction and symmetry breaking
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Fermions on spontaneously generated spherical extra dimensions
• Orbifolds, fuzzy spheres and chiral fermions
• On the fermion spectrum of spontaneously generated fuzzy extra dimensions with fluxes
• Dynamical generation of gauge groups in the massive Yang-Mills-Chern-Simons matrix model
• Noncommutative gauge theory and symmetry breaking in matrix models
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• Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking
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• Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory
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• Gauge Theories and Non-Commutative Geometry
• Observable-enriched entanglement
• Equivariance on Discrete Space and Yang-Mills-Higgs Model