Liouville theory and uniformization of four-punctured sphere

Details Liouville theory and uniformization of four-punctured sphere Liouville theory and uniformization of four-punctured sphere

2006-04-25

arxiv.org/abs/hep-th/0604187v1

J.Math.Phys.47:082304,2006

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, no figures

Scientific paper

Few years ago Zamolodchikov and Zamolodchikov proposed an expression for the 4-point classical Liouville action in terms of the 3-point actions and the classical conformal block. In this paper we develop a method of calculating the uniformizing map and the uniformizing group from the classical Liouville action on n-punctured sphere and discuss the consequences of Zamolodchikovs conjecture for an explicit construction of the uniformizing map and the uniformizing group for the sphere with four punctures.

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