On the rigorous construction of Liouville theory via the conformal bootstrap:
Colin Guillarmou, Rémi Rhodes, Vincent Vargas, Polyakov’s formulation of 2d bosonic string theory, Publ. Math. IHES 130 (2019) 111–185 [arXiv:1607.08467, doi:10.1007/s10240-019-00109-6]
Colin Guillarmou, Antti Kupiainen, Rémi Rhodes, Vincent Vargas, Conformal bootstrap in Liouville Theory (arxiv:2005.11530)
and as a functorial field theory following Segal 1988:
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