Open String Field Theory on Noncommutative Space

TL;DR

This paper explores how a constant B field affects Witten's open string field theory, revealing noncommutative zero modes and discussing background independence and supersymmetric extensions.

Contribution

It constructs a modified string field theory incorporating a B field, showing the emergence of noncommutative zero modes and proposing a redefinition to remove additional factors.

Findings

Vertices acquire an additional factor due to the B field

Zero modes become noncommutative in the presence of B field

Background independence is discussed and a field redefinition is proposed

Abstract

We study Witten's open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting theory has an additional factor. The factor makes the zero modes of strings noncommutative. This is in agreement with the results in the first-quantized formulation. We also discuss background independence of the purely cubic action derived from the above string field theory and then find a redefinition of string fields to remove the additional factor from the vertex. Furthermore, we briefly discuss the supersymmetric extension of our string field theory.