VORTICES AND MONOPOLES IN LIOUVILLE THEORY

We consider applications of recent results describing Kosterlitz-Thouless type phase transitions of vortices and monopoles defined on a two dimensional space of spherical topology. It is argued that bosonic Liouville theory, and its N = 1 supersymmetric generalization, are in the strong coupling phase unless D < 1. For the N = 2 theory, however, it is unlikely that such a restriction is necessary; the theory being in the weak phase for any value of D.