Fuzzy Conifold $Y_F^6$ and Monopoles on $S_F^2\times S_F^2$

In this article, we construct the fuzzy (finite dimensional) analogues of the conifold $Y^6$ and its base $X^5$. We show that fuzzy $X^5$ is (the analogue of) a principal U(1) bundle over fuzzy spheres $S_F^2\times S_F^2$ and explicitly construct the associated monopole bundles. In particular our construction provides an explicit discretization of the spaces $T^{\kappa ,\kappa }$ and $T^{\kappa ,0}$.