Renormalizable Theories from Fuzzy Higher Dimensions

Abstract

We consider gauge theories defined in higher dimensions where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized `a la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i) the appearance of non-abelian gauge theories in four dimensions starting from an abelian gauge theory in higher dimensions, (ii) the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii) the renormalizability of the theory both in higher as well as in four dimensions.

11 pages. Based on invited lectures given by John Madore and George Zoupanos in the III Summer School in Modern Mathematical Physics, Zlatibor, Serbia, 20-31.08.2004

References in corpus (4)

• Quantized Gauge Theory on the Fuzzy Sphere as Random Matrix Model
• General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory
• Finite Gauge Theory on Fuzzy CP^2
• Running couplings in extra dimensions

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• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• An invariant approach to dynamical fuzzy spaces with a three-index variable -- Euclidean models
• Equivariant Reduction of U(4) Gauge Theory over S_F^2 x S_F^2 and the Emergent Vortices
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• Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories
• 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