Curvature Singularity as the Vertex Operator

TL;DR

This paper investigates how a point-like singularity in a 2D conformal field theory's manifold affects the vacuum state and correlation functions, revealing the emergence of an effective mass and the need for modified theoretical considerations.

Contribution

It demonstrates how a singular metric alters the vacuum and correlation functions in 2D CFT, introducing an effective mass and non-invariance under SL(2,C).

Findings

Vacuum state differs from BPZ theory on singular surfaces.

Correlation functions require modification due to singularity.

An effective mass term emerges from the singularity.

Abstract

The submitted paper regards the example of the Conformal Field Theory on a 2d manifold which metric has a point-like singularity.Since this manifold is not conformally equivalent to that with the flat space-time metric,it's naturally to expect that the theory cannot be trivially reduced to the well-known consideration of the CFT on a plane,and some modifications are needed.Particularly,this paper shows how the vacuum of the theory on a singular surface differs from the vacuum of the BPZ theory.Namely,this vacuum would not be SL(2,C)-invariant and the expressions for the correlation functions should be modified. As a consequence of that,some "effective mass" is brought to the theory.