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

TL;DR

This paper constructs fuzzy finite-dimensional analogues of the conifold and its base, demonstrating a principal U(1) bundle structure over fuzzy spheres and explicitly building monopole bundles, thus discretizing certain geometric spaces.

Contribution

It introduces a novel fuzzy model of the conifold and its base, including explicit monopole bundle constructions and discretizations of specific geometric spaces.

Findings

Fuzzy analogues of the conifold and base are constructed.

Explicit monopole bundles over fuzzy spheres are developed.

Discretization of spaces T^{ppa,ppa} and T^{ppa,0} is achieved.

Abstract

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 $S^2_F \times S^2_F$ and explicitly construct the associated monopole bundles. In particular our construction provides an explicit discretization of the spaces $T^{\kappa,\kappa}$ and $T^{\kappa,0}$.