Group theoretical derivation of Liouville action for Regge surfaces

TL;DR

This paper derives the Liouville action for Regge surfaces of sphere and torus topology using symmetry principles, specifically conformal Killing vectors and modular invariance.

Contribution

It provides a group-theoretical derivation of the Liouville action tailored for Regge surfaces, highlighting the role of symmetry constraints.

Findings

Liouville action structure is dictated by conformal and modular invariance.

The derivation applies to both spherical and toroidal topologies.

Symmetry considerations uniquely determine the form of the action.

Abstract

We show that the structure of the Liouville action on a two dimensional Regge surface of the topology of the sphere and of the torus is determined by the invariance under the transformations induced by the conformal Killing vector fields and under modular transformations.