Open-Closed String Field Theory in the Background B-Field

TL;DR

This paper explores the relationship between two formulations of open-closed string field theory in a B-field background, demonstrating their equivalence through a unitary transformation, and connecting noncommutative gauge theory with a commutative counterpart.

Contribution

It introduces and proves the equivalence of two different string field theories in the same background, one exhibiting noncommutativity and the other not, via explicit unitary transformation.

Findings

The infrared limit yields noncommutative gauge theory.

Closed string field condensation leads to a commutative effective theory.

The two formulations are shown to be unitarily equivalent.

Abstract

In this paper, we study open-closed string field theory in the background B-field in the so-called alpha=p^{+} formulation. The string field theory in the infrared gives noncommutative gauge theory in the open string sector. Since this theory includes closed string fields as dynamical variables, we can obtain another string field theory in the same background through the condensation of closed string fields, whose low-energy effective action does not show the noncommutativity of spacetime. Although we have two string field theories in the same background, we show that these theories are equivalent. In fact, we give the unitary transformation from string fields in one of them to string fields in the other.