Monopoles On $S^2_F$ From The Fuzzy Conifold

TL;DR

This paper constructs and analyzes monopoles on the fuzzy sphere $S^2_F$ derived from the conifold intersection, providing a new fuzzy geometric realization and monopole line bundles with even charges.

Contribution

It introduces a novel fuzzy geometric construction of monopoles on $S^2_F$ using the conifold intersection and Kaluza-Klein reduction techniques.

Findings

Monopoles on $S^2_F$ have only even integer charges.

A new fuzzy realization of the $S^2$ fibration and line bundles.

Explicit construction of monopoles via the fuzzy conifold approach.

Abstract

The intersection of the conifold $z_1^2+z_2^2+z_3^2 =0$ and $S^5$ is a compact 3--dimensional manifold $X^3$. We review the description of $X^3$ as a principal U(1) bundle over $S^2$ and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza--Klein reduction of $X^3$ to $S^2$ provides an easy construction of these monopoles. Using the analogue of the Jordon-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration $X^3 \rightarrow S^2$ and the associated line bundles. This is an alternative new realization of the fuzzy sphere $S^2_F$ and monopoles on it.