Topological Charges of Noncommutative Soliton

TL;DR

This paper explores the topological charges of noncommutative solitons using K-theory, revealing how projection operators relate to brane charge modifications in string theory with tachyon backgrounds.

Contribution

It introduces a method to identify topological charges of noncommutative solitons via K-theory and applies this to string theory to analyze brane charge modifications.

Findings

Topological charges are characterized by projection operators in noncommutative space.

Variations of projection operators relate to topological charge changes.

Application to string theory shows modified brane charges due to tachyon backgrounds.

Abstract

The noncommutative soliton is characterized by the use of the projection operators in non-commutative space. By using the close relation with the K-theory of $C^*$-algebra, we consider the variations of projection operators along the commutative directions and identify their topological charges. When applied to the string theory, it gives the modification of the brane charges due to tachyon background.