CURVATURE SINGULARITY AS A VERTEX OPERATOR

The 2d theory of free massless bosons, as an example of CFT, is discussed on a manifold with a point-like singularity in the curvature. We argue that such a singularity can be represented as a non-local vertex operator inserted in the theory. This representation makes it possible to get all the correlation functions. It is shown how the presence of a ''needle'' in the geometry of the surface produces a breakdown of the conformal symmetry. Examples of the correlators are derived.