On the rigorous construction of Liouville theory
François David, Antti Kupiainen, Rémi Rhodes, Vincent Vargas, Liouville Quantum Gravity on the Riemann sphere, Communications in Mathematical Physics volume 342, pages869–907 (2016) (arxiv:1410.7318)
Antti Kupiainen, Rémi Rhodes, Vincent Vargas, Integrability of Liouville theory: proof of the DOZZ Formula, Annals of Mathematics, Pages 81-166 from Volume 191 (2020), Issue 1, (arxiv:1707.08785, doi:10.4007/annals.2020.191.1.2)
Antti Kupiainen, Rémi Rhodes, Vincent Vargas, The DOZZ formula from the path integral, Journal of High Energy Physics volume 2018, Article number: 94 (2018) (arXiv:1803.05418 doi:10.1007/JHEP05(2018)094)
and via the conformal bootstrap:
and as a functorial field theory following Segal 1988:
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