The DOZZ Formula from the Path Integral

TL;DR

This paper provides a rigorous probabilistic proof of the DOZZ formula, which determines the 3-point structure constants in Liouville Conformal Field Theory, using advanced tail analysis of Gaussian multiplicative chaos.

Contribution

It offers the first rigorous derivation of the DOZZ formula from a probabilistic perspective, connecting functional integral construction with Gaussian chaos techniques.

Findings

Proof of the DOZZ formula from probabilistic methods

Probabilistic derivation of the reflection relation in LCFT

Refined tail analysis of Gaussian multiplicative chaos measures

Abstract

We present a rigorous proof of the Dorn, Otto, Zamolodchikov, Zamolodchikov formula (the DOZZ formula) for the 3 point structure constants of Liouville Conformal Field Theory (LCFT) starting from a rigorous probabilistic construction of the functional integral defining LCFT given earlier by the authors and David. A crucial ingredient in our argument is a probabilistic derivation of the reflection relation in LCFT based on a refined tail analysis of Gaussian multiplicative chaos measures.