Quantum Liouville field theory as solution of a flow equation Original Research Article

A general framework for the Weyl-invariant quantization of Liouville field theory by means of an exact renormalization group equation is proposed. This renormalization group, or flow equation, describes the scale dependence of the effective average action which has a built-in infrared cutoff. For c < 1 it is solved approximately by a truncation of the space of action functionals. We derive the Ward identities associated to Weyl transformations in the presence of the infrared cutoff. They are used to select a specific universality class for the renormalization group trajectory which is found to connect two conformal field theories with central charges 25 - c and 26 - c, respectively.