Negative Screenings in Liouville Theory

TL;DR

This paper explains the emergence of negative screening powers in Liouville theory as a nonperturbative effect, leading to a direct computation of the three-point function that supports the DOZZ conjecture without analytic continuation.

Contribution

It introduces a nonperturbative operator approach to Liouville theory that accounts for negative screenings and computes the three-point function directly, confirming the DOZZ formula.

Findings

Negative screenings arise as nonperturbative effects in Liouville theory.

The three-point function is computed without analytic continuation, supporting the DOZZ conjecture.

Free field expansions with adjustable monodromies unify different local observables.

Abstract

We demonstrate how negative powers of screenings arise as a nonperturbative 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 $(\hbox{Zamolodchikov})^2$ (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.