Virasoro-Shapiro from Wilson

We develop the proposal of Banks and Martinec that the string field equation can be written as an infinite dimensional renormalization group equation. We generalize the Wilson equation to conformal invariance and to open strings, and make a preliminary study of the gauge invariance and auxiliary fields. To obtain the S-matrix, we first study the relation between field equations and S-matrices in general field theories. We then give a general demonstration that the field equations from world-sheet conformal invariance agree with the string S-matrix at tree level. (orig.)