Non-perturbative formulation of non-critical string models

We apply to non-critical bosonic Liouville string models, characterized by acentral-charge deficit Q, a new non-perturbative renormalization-grouptechnique based on a functional method for controlling the quantumfluctuations. We demonstrate the existence of a renormalization-group fixedpoint of Liouville string theory as Q to 0, in which limit the targetspace-time is Minkowski and the dynamics of the Liouville field is trivial, asit neither propagates nor interacts. This calculation supports in a non-trivalmanner the identification of the zero mode of the Liouville field with thetarget time variable, up to a crucial minus sign.Comment: 16 pages latex, 2 eps figure