Higher-Dimensional Unified Theories with Fuzzy Extra Dimensions

Abstract

Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle physics models in the context of higher-dimensional gauge theories with non-commutative extra dimensions. These ideas have been developed in two complementary ways, namely (i) starting with a higher-dimensional gauge theory and dimensionally reducing it to four dimensions over fuzzy internal spaces and (ii) starting with a four-dimensional, renormalizable gauge theory and dynamically generating fuzzy extra dimensions. We describe the above approaches and moreover we discuss the inclusion of fermions and the construction of realistic chiral theories in this context.

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Cited by in corpus (13)

• Matricial bridges for "Matrix algebras converge to the sphere"
• $N=1$ trinification from dimensional reduction of $N=1$, $10D$ $E_8$ over $SU(3)/U(1)\times U(1)\times Z_3$ and its phenomenological consequences
• On Lie-algebraic solutions of the type IIB matrix model
• Higher-Dimensional Unification with continuous and fuzzy coset spaces as extra dimensions
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• Vector bundles for "Matrix algebras converge to the sphere"
• 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
• 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
• Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions
• Observable-enriched entanglement
• Equivariance on Discrete Space and Yang-Mills-Higgs Model