Non-commutative space and Chan–Paton algebra in open string field algebra

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.

Chan-Paton factors and higgsing from vacuum string field theory

“…This fact is hardly a surprise given that the field redefinition relating OSFT on the tachyon vacuum to VSFT completely shrinks the body of a string to its midpoint and "resolves" the endpoints into the left/right halves, [20]. This, we believe, is the reason why Chan-Paton factors are to be found in left/right excitations of VSFT classical solutions, and not in the endpoints, see [31].…”

“…Note that the left/right structure of these states is the same as a U(N) double line notation, as the relations (3.12) certify. It should be noted that this Chan-Paton structure does not sit at the endpoints of the string, [31], but is rather "diluted" on the string halves. This can be traced back to the singular field redefinition that should relate OSFT with VSFT, see the conclusions.…”

Analytical Solutions of Open String Field Theory

“…45 The treatment of a B-field background in string theory in the language of noncommutative field theory was developed in [19]. The implementation of this idea within string field theory was studied in [184,185,186,187,188,189]. 46 See [190] for a general study of boundary deformations.…”