The conformal properties of Liouville field theory on ZN-Riemann surfaces

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.