Construction of fuzzy S^4

Details Construction of fuzzy S^4 Construction of fuzzy S^4

2004-06-15

arxiv.org/abs/hep-th/0406135v3

Phys.Rev. D70 (2004) 126004

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.70.126004

We construct a fuzzy $S^4$, utilizing the fact that ${\bf CP}^3$ 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 ${\bf CP}^3$. 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 ${\bf CP}^7$ is a ${\bf CP}^3$ bundle over $S^8$.

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