Witten's Open String Field Theory in Constant B-Field Background

TL;DR

This paper explores Witten's open string field theory in a constant B-field background, revealing a Moyal-type noncommutative structure in the zero-mode sector and connecting it to gauge theory transformations.

Contribution

It extends the operator formulation of string field theory to include a constant B-field and identifies the noncommutative structure and its relation to gauge transformations.

Findings

Noncommutative Moyal structure appears in zero-mode sector

A unitary transformation absorbs the noncommutative structure

Connection to Seiberg-Witten gauge theory transformation

Abstract

In this paper we consider Witten's bosonic open string field theory in the presence of a constant background of the second-rank antisymmetric tensor field $B_{ij}$. We extend the operator formulation of Gross and Jevicki in this situation and construct the overlap vertices explicitly. As a result we find a noncommutative structure of the Moyal type only in the zero-mode sector, which is consistent with the result of the correlation functions among vertex operators in the world sheet formulation. Furthermore we find out a certain unitary transformation of the string field which absorbs the Moyal type noncommutative structure. It can be regarded as a microscopic origin of the transformation between the gauge fields in commutative and noncommutative gauge theories discussed by Seiberg and Witten.