Towards a Strong Coupling Liouville Gravity

TL;DR

This paper explores the theoretical framework of strong coupling quantum Liouville gravity using infinite dimensional representations of quantum groups at roots of unity, revealing a tensor product structure of vertex operators.

Contribution

It introduces a novel approach to strong coupling Liouville gravity through quantum group representations, connecting classical and quantum Liouville theories.

Findings

Vertex operators can be expressed as tensor products of classical and weak coupling quantum Liouville operators.

The formulation provides insights into the structure of strong coupling Liouville gravity.

Discussions on the implications of this approach for the theory's development.

Abstract

A possibility of strong coupling quantum Liouville gravity is investigated via infinite dimensional representations of $\qslc$ with $q$ at a root of unity. It is explicitly shown that vertex operator in this model can be written by a tensor product of a vertex operator of the classical Liouville theory and that of weak coupling quantum Liouville theory. Some discussions about the strong coupling Liouville gravity within this formulation are given.