The DOZZ Formula from the Path Integral

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.

References in corpus (3)

• Correlation functions in conformal Toda field theory II
• Multipoint correlation functions in Liouville field theory and minimal Liouville gravity
• Renormalizability of Liouville Quantum Gravity at the Seiberg bound

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• Mating of trees for critical Liouville quantum gravity