The off-shell vertex in conformal field theory and string field theory

Abstract

It is shown that while the usual β-functions approach gives interacting equations of motion that are only valid as small perturbations around the free equations, there is a simple modification that allows one to go off the free mass shell. This involves computing correlation functions of vertex operators that are separated by distances on the order of the lattice spacing — which is equivalent to studying the renormalization group equations with a finite cutoff. Applying this technique to the tachyon equation of motion, in the light cone gauge, we reproduce the off-shell three-tachyon aned vector-tachyon-tachyon vertices of (light cone gauge) open string field theory.