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

TL;DR

This paper constructs a Spin(5) invariant fuzzy $CP^3$ as an $S^2$ bundle over fuzzy $S^4$, developing scalar and spinor actions with low-energy modes approximating those of a commutative $S^4$.

Contribution

It introduces a new fuzzy $CP^3$ model as an $S^2$ bundle over fuzzy $S^4$ with explicit projectors and squashing parameters.

Findings

Constructed scalar and spinor fuzzy actions with low-energy modes

Provided explicit projectors and squashing parameters

Demonstrated the model's approximation to commutative $S^4$

Abstract

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 $S^4$.