Kupiainen, Antti; Rhodes, Rémi; Vargas, Vincent Integrability of Liouville theory: proof of the DOZZ formula. (English) Zbl 1432.81055 Ann. Math. (2) 191, No. 1, 81-166 (2020). The paper under review is written by experts in the area of Liouville quantum gravity, quantum fields theory, BPZ equations. The main purpose of authors is to prove the equivalence of the Dorn, Otto, Zamolodchikov and Zamolodchkov (DOZZ) formula from a statistical standpoint, namely from the standpoint of Liouville conformal field theory. To my opinion the authors successfully proved the formula. Reviewer: Alex B. Gaina (Chisinau) Cited in 2 ReviewsCited in 21 Documents MSC: 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 81Q50 Quantum chaos 81V17 Gravitational interaction in quantum theory 83C45 Quantization of the gravitational field Keywords:Liouville quantum gravity; quantum field theory; Gaussian multiplicative chaos; Ward identities; BPZ equations; DOZZ formula PDF BibTeX XML Cite \textit{A. Kupiainen} et al., Ann. Math. (2) 191, No. 1, 81--166 (2020; Zbl 1432.81055) Full Text: DOI arXiv Link OpenURL