Construction of fuzzy S^4

Abstract

We construct a fuzzy $S^4$, utilizing the fact that ${\mathbf{CP}}^3$ is an $S^2$ bundle over $S^4$. We find that a fuzzy $S^4$ can be described by a block-diagonal form whose embedding square matrix represents a fuzzy ${\mathbf{CP}}^3$. We discuss some pending issues on fuzzy $S^4$, i.e., precise matrix-function correspondence, associativity of the algebra, and etc. Similarly, we also obtain a fuzzy $S^8$, using the fact that ${\mathbf{CP}}^7$ is a ${\mathbf{CP}}^3$ bundle over $S^8$.

17 pages; v2. extensively rewritten; v3. published version

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• Pair double heavy diquark production in high energy proton-proton collisions
• Explicit Non-Abelian Monopoles and Instantons in SU(N) Pure Yang-Mills Theory
• Higher spin gauge theory on fuzzy $S_N^4$
• One-loop stabilization of the fuzzy four-sphere via softly broken SUSY
• Evolving fuzzy CP^n and lattice n-simplex
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• Fuzzy Torus via q-Parafermion
• Branes, Quantization and Fuzzy Spheres
• Emergence of longitudinal 7-branes and fuzzy S^4 in compactification scenarios of M(atrix) theory