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.
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ArXiv ePrint: 1803.05418
Supported by the Academy of Finland and ERC Advanced Grant 741487. (Antti Kupiainen)
Partially supported by grant ANR-15-CE40-0013 Liouville. (Rémi Rhodes)
Partially supported by grant ANR-15-CE40-0013 Liouville. (Vincent Vargas)
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Kupiainen, A., Rhodes, R. & Vargas, V. The DOZZ formula from the path integral. J. High Energ. Phys. 2018, 94 (2018). https://doi.org/10.1007/JHEP05(2018)094
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DOI: https://doi.org/10.1007/JHEP05(2018)094