Sewing Polyakov amplitudes I: Sewing at a fixed conformal structure

Abstract

We consider the problem of reconstructing the correlation functions of a conformal field theory on a surface Σ from the correlation functions on a surface Σ′ obtained from Σ by cutting along a closed curve. We show that under quite general conditions, the correlation functions on the cut surface can be "sewn" by integrating over appropriate boundary valuess of the field. © 1990 Springer-Verlag.