Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality

TL;DR

This paper formulates the strongly coupled quantum discrete Liouville theory as a well-defined quantum system, revealing its self-duality and algebraic structure, and establishing a foundation for further analysis of its properties.

Contribution

It introduces an algebraic approach to the strongly coupled regime of quantum discrete Liouville theory, demonstrating its self-duality and the structure of its observables.

Findings

The theory is well-defined with a unitary evolution operator.

It exhibits self-duality with two related exponential fields.

The fields satisfy two discrete quantum Liouville equations.

Abstract

The quantum discrete Liouville model in the strongly coupled regime, 1<c<25, is formulated as a well defined quantum mechanical problem with unitary evolution operator. The theory is self-dual: there are two exponential fields related by Hermitean conjugation, satisfying two discrete quantum Liouville equations, and living in mutually commuting subalgebras of the quantum algebra of observables.