2012

Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $CP^3$ as a $S^2_F$ bundle over $S^4_F$

Medina, Julieta, Huet, Idrish, O'Connor, Denjoe et al.

Understand

We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ 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 $S^4$.

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