The DOZZ Formula from the Path Integral
High Energy Physics - Theory
2018-06-13 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1803.05418,
title = {The DOZZ Formula from the Path Integral},
author = {Antti Kupiainen and Rémi Rhodes and Vincent Vargas},
journal= {arXiv preprint arXiv:1803.05418},
year = {2018}
}