Liouville Field Theory on Hyperelliptic surface

TL;DR

This paper explores Liouville field theory on hyperelliptic surfaces, expressing its partition function through correlation functions involving vertex and twist fields, thus extending the understanding of Liouville theory in complex geometries.

Contribution

It provides a novel formulation of the Liouville partition function on hyperelliptic surfaces using correlation functions with vertex and twist fields.

Findings

Partition function expressed as correlation functions on sphere

Connection between hyperelliptic surfaces and Liouville vertex/twist fields

Extension of Liouville theory to complex geometries

Abstract

Liouville field theory on hyperelliptic surface is considered. The partition function of the Liouville field theory on the hyperelliptic surface are expressed as a correlation function of the Liouville vertex operators on a sphere and the twist fields.