SOLVING THE STRONGLY COUPLED 2D GRAVITY .2. FRACTIONAL-SPIN OPERATORSAND TOPOLOGICAL 3-POINT FUNCTIONS

We report progress along the line of a previous article-the first of t he series-by one of us (J. L.G.). One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of inte gers) which are needed to achieve the necessary correspondence between the set of conformal weights of primaries and the physical spectrum o f Virasoro highest weights. This is possible by extending the study of the chiral bootstrap (recently completed by Cremmer, and the present authors) to the case of semi-infinite quantum-group representations wh ich correspond to positive integral screening numbers. In particular, we prove the Bidenham-Elliot and Racah identities for q-deformed 6-j s ymbols generalized to continuous spins. The decoupling of the family o f physical chiral operators (with real conformal weights) at the speci al values C-Liouville = 7, 13, and 19, is shown to provide a full solu tion of Moore and Seiberg's equations, only involving operators with r eal conformal weights. Moreover, our study confirms the existence of t he strongly coupled topological models put forward earlier. The three- point functions are determined. They are given by a product of leg fac tors similar to the ones of the weakly coupled models. However, contra ry to this latter case, the equality between the quantum group spins o f the holomorphic and antiholomorphic components is not preserved by t he local vertex operator. Thus the ''c = 1'' barrier appears as connec ted with a deconfinement of chirality.