Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-09-23
J.Geom.Phys. 29 (1999) 161-176
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, plain TeX + harvmac
Scientific paper
A new approach to analyze the properties of the energy-momentum tensor $T(z)$ of conformal field theories on generic Riemann surfaces (RS) is proposed. $T(z)$ is decomposed into $N$ components with different monodromy properties, where $N$ is the number of branches in the realization of RS as branch covering over the complex sphere. This decomposition gives rise to new infinite dimensional Lie algebra which can be viewed as a generalization of Virasoro algebra containing information about the global properties of the underlying RS. In the simplest case of hyperelliptic curves the structure of the algebra is calculated in two ways and its central extension is explicitly given. The algebra possess an interesting symmetry with a clear interpretation in the framework of the radial quantization of CFT's with multivalued fields on the complex sphere.
Ferrari Franco
Sobczyk Jan T.
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