Abstract :
We demonstrate how negative powers of screenings arise as a non-perturbative effect within the operator approach to Liouville theory. This explains the origin of the corresponding poles in the exact Liouville three-point function proposed by Dorn/Otto and (Zamolodchikov)2 (DOZZ) and leads to a consistent extension of the operator approach to arbitrary integer numbers of screenings of both types. The general Liouville three-point function in this setting is computed without any analytic continuation procedure, and found to support the DOZZ conjecture. We point out the importance of the concept of free-field expansions with adjustable monodromies - recently advocated by Petersen, Rasmussen and Yu - in the present context, and show that it provides a unifying interpretation for two types of previously constructed local observables.
