On the background independence of string field theory

Abstract

Given a solution ψ_cl of the classical equations of motion in either closed or open string field theory formulated around a given conformal field theory background, we can construct a new operator Q^{^}_B in the corresponding two-dimensional field theory such that (Q^{^}_B)²=0. It is shown that in the limit when the background field ψ_cl is weak, Q^{^}_B can be identified with the BRST charge of a new local conformal field theory. This indicates that the string field theories formulated around these two different conformal field theories are actually the same theory, and that these two conformal field theories may be regarded as different classical solutions of this string field theory.