The Conformal Properties of Liouville Field Theory on Z_N-Riemann Surfaces

TL;DR

This paper investigates Liouville field theory on Z_N-Riemann surfaces, revealing its decomposition into simpler theories and expressing its partition function as a product involving sphere correlation functions and twisted fields.

Contribution

It demonstrates the decomposition of Liouville theory on Z_N-Riemann surfaces into a sphere theory and free bosons, and formulates its partition function in terms of sphere correlation functions.

Findings

Liouville theory decomposes into sphere and free boson theories.

Partition function expressed as a product of sphere correlation functions and twisted fields.

Provides a new understanding of Liouville theory on Z_N-Riemann surfaces.

Abstract

The Liouville field theory on Z_N-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 Z_N-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.