Fuzzy Line Bundles, the Chern Character and Topological Charges over the Fuzzy Sphere

TL;DR

This paper computes the Chern characters and topological charges of noncommutative line bundles over the fuzzy sphere, revealing non-integer values that approach integer Chern numbers in the classical limit.

Contribution

It introduces a method to determine Chern characters of all noncommutative line bundles over the fuzzy sphere using quantized equivariant vector bundles.

Findings

Chern numbers are non-integer for fuzzy sphere bundles

Classical integer Chern numbers are recovered in the commutative limit

Provides a comprehensive calculation of topological charges in noncommutative geometry

Abstract

Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The associated Chern numbers (topological charges) arise to be non-integer, in the commutative limit the well known integer Chern numbers of the complex line bundles over the 2-sphere are recovered.