ON THE FUSION RULES OF CONFORMAL MATTER COUPLED TO 2D QUANTUM-GRAVITY

An analysis of the conformal blocks of the minimal Ising model coupled to the Liouville theory with zero cosmological constant shows that the free theory has some features recently found in the interacting one. Namely, the null states of the matter theory appear as intermediate states at the dominant level. States of the form (0, n) living in the boundary of the Kac formula also show up as physical states.