Non-commutative Space And Chan-Paton Algebra In Open String Field Algebra

TL;DR

This paper explores the equivalence of different descriptions of open string backgrounds involving non-commutative geometry and Chan-Paton algebra within Witten's cubic open string field theory, identifying their algebraic structures.

Contribution

It demonstrates the correspondence between non-commutative coordinate algebra, Chan-Paton matrix algebra, and open string field algebra, establishing their equivalence in string theory backgrounds.

Findings

Non-commutative coordinates form a subalgebra of open string field algebra.

Chan-Paton matrix algebra is identified as a subalgebra of open string field algebra.

Different descriptions of open string backgrounds are shown to be equivalent through algebraic mappings.

Abstract

There are several equivalent descriptions for constant B-field background of open string. The background can be interpreted as constant B-field as well as constant gauge field strength or infinitely many D-branes with non-commuting Chan-Paton matrices. In this article, the equivalence of these open string theories is studied in Witten's cubic open string field theory. Through the map between these equivalent descriptions, both algebra of non-commutative coordinates as well as Chan-Paton matrix algebra are identified with subalgebras of open string field algebra.