Exact Operator Solution for Liouville Theory with $q$ A Root of Unity

Abstract

The exact operator solution for quantum Liouville theory constructed for the generic quantum deformation parameter $q$ is extended to the case with $q$ being a root of unity. The screening charge operator becomes nilpotent in such cases and arbitrary Liouville exponentials can be obtained in finite polynomials of the screening charge.

This paper is withdrawn due to the incorrect handling of some formulas