Noncommutative Solitons on Orbifolds

TL;DR

This paper explores the algebraic description of D-branes as noncommutative solitons on orbifolds, extending the framework to include asymmetric orbifolds and providing a unified algebraic approach.

Contribution

It introduces a natural algebraic framework for D-branes on orbifolds within noncommutative field theory, including new proposals for asymmetric orbifolds.

Findings

D-branes are described as projection operators in $C^*$ algebras.

The framework applies to orbifolds like $R^n/G$, $T^n=R^n/Z^n$, and $T^n/G$.

A new approach for D-branes on asymmetric orbifolds is proposed.

Abstract

In the noncommutative field theory of open strings in a B-field, D-branes arise as solitons described as projection operators or partial isometries in a $C^*$ algebra. We discuss how D-branes on orbifolds fit naturally into this algebraic framework, through the examples of $R^n/G$, $T^n=R^n/Z^n$, and $T^n/G$. We also propose a framework for formulating D-branes on asymmetric orbifolds.