Topological Z_{N+1} Charges on Fuzzy Sphere

TL;DR

This paper explores the topological charges on fuzzy spheres, revealing a modulo N+1 structure, and connects these findings to K-theory and D-brane solitons in string theory.

Contribution

It demonstrates that topological charges on fuzzy spheres are classified by Z_{N+1} and relates this to twisted K-theory and D-brane solitons.

Findings

Topological charge is defined modulo N+1.

The periodic structure is derived from boson realizations of SU(2).

Connections to twisted K-theory and D-brane solitons are proposed.

Abstract

We study the topological properties of fuzzy sphere. We show that the topological charge is only defined modulo N+1, that is finite integer quotient Z_{N+1}, where N is a cut-off spin of fuzzy sphere. This periodic structure on topological charges is shown based on the boson realizations of SU(2) algebra, Schwinger vs. Holstein-Primakoff. We argue that this result can have a natural K-theory interpretation and the topological charges on fuzzy sphere can be classified by the twisted K-theory. We also outline how solitons on fuzzy sphere can realize D-brane solitons in the presence of Neveu-Schwarz fivebranes proposed by Harvey and Moore.