Strongly Coupled Quantum Discrete Liouville Theory. II: Geometric Interpretation of the Evolution Operator

TL;DR

This paper demonstrates that the N-th power of the light-cone evolution operator in a quantum discrete Liouville model corresponds to the Dehn twist operator in quantum Teichmuller theory, revealing a deep geometric connection.

Contribution

It establishes a precise identification between the evolution operator in quantum Liouville theory and a fundamental geometric operation in quantum Teichmuller theory.

Findings

N-th power of the evolution operator equals the Dehn twist operator

Links quantum discrete Liouville theory with quantum Teichmuller geometry

Provides a geometric interpretation of quantum evolution in Liouville theory

Abstract

It is shown that the N-th power of the light-cone evolution operator of 2N-periodic quantum discrete Liouville model can be identified with the Dehn twist operator in quantum Teichmuller theory.