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arXiv · hep-th/9302017

Curvature Singularity as the Vertex Operator

Dimitri Polyakov
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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.

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Dimitri Polyakov. 1993-02-13. Curvature Singularity as the Vertex Operator. https://doi.org/10.1016/0550-3213(93)90319-k

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