Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $C{P}^3$ as a $S_F^2$ bundle over $S_F^4$

Abstract

We present a manifestly Spin(5) invariant construction of squashed fuzzy $C{P}^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative $S^4$.

19 pages

References in corpus (4)

• A universal Dirac operator and noncommutative spin bundles over fuzzy complex projective spaces
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Spin $j$ Dirac Operators on the Fuzzy 2-Sphere
• A projective Dirac operator on CP^2 within fuzzy geometry

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• A Twistorial Description of the IKKT-Matrix Model
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• Higher spin gauge theory on fuzzy $S_N^4$
• Intertwining noncommutativity with gravity and particle physics
• Dirac operators for matrix algebras converging to coadjoint orbits
• Emergent fuzzy geometry and fuzzy physics in $4$ dimensions