1998•Physics Letters BOpen access

The conformal properties of Liouville field theory on -Riemann surfaces

S. A. Apikyan, Costas John Efthimiou

Abstract

The Liouville field theory on ZN-Riemann surfaces is studied and it is shown that it decomposes into a Liouville field theory on the sphere and N−1 free boson theories. Also, the partition function of the Liouville field theory on the ZN-Riemann surfaces is expressed as a product of the correlation function for the Liouville vertex operators on the sphere and a number of twisted fields.

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Key concepts: Liouville field theory, Conformal field theory, Riemann surface, Riemann sphere, Partition function (quantum field theory), Mathematics, Mathematical physics, Geometric function theory