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Scalar and spinor field actions on fuzzy \(S^4\): fuzzy \(\mathbb{C} P^3\) as a \(S^2_F\) bundle over \(S^4_F\). (English) Zbl 1397.81417
Summary: We present a manifestly Spin(5) invariant construction of squashed fuzzy \(\mathbb{C} P^3\) 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 \(S^4\).

81T75 Noncommutative geometry methods in quantum field theory
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