Monopoles On $S_F^2$ From The Fuzzy Conifold

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 $X^3\to S^2$ and the associated line bundles. This is an alternative new realization of the fuzzy sphere $S_F^2$ and monopoles on it.

version submitted to JHEP

References in corpus (2)

• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Noncommutative Vortices and Instantons from Generalized Bose Operators

Cited by in corpus (2)

• Quantum Entropy for the Fuzzy Sphere and its Monopoles
• Monopoles, Dirac operator and index theory for fuzzy $SU(3)/(U(1)\times U(1))$