On the background independence of string field theory: II. Analysis of on-shell S-matrix elements

Abstract

Given a solution ψ_cl of the classical equations of motion in either closed or open string field theory based on a certain conformal field theory (CFT) we may define a shifted string field ψ^{^}=ψ−ψ_cl. The string field theory action expressed interms of the shifted field is then given by S^{^}(ψ^{^})=S(ψ^{^}+ψ_cl−S(ψ_cl), where S(ψ) is the original action of the string field theory. In S(ψ^{^}) the coefficient (Q^{^}_B) of the quadratic term ψ^{^} in has the property that (Q^{^}_B)₂=0. It was shown in a previous paper that in the limit when the background ψ_cl is weak, Q^{^}_B can be identified with the BRST charge of a new conformal field theory (CFT"), which is obtained by perturbing the orginal conformal field theory (CTF) by a marginal operator. In this paper we compute various on-shell S-matrix elements using the action S^{^} (ψ^{^}) and show that they are identical to the on-shell S-matrix in the string based on the new conformal field theory (CTF"). This in turn shows that S^{^}(ψ^{^}) describes string theory formulated around the background of this new conformal field theory.