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

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