Integrability of Liouville theory: the Kupiainen–Rhodes–Vargas proof of the DOZZ formula
A Lean 4 / Mathlib formalization of the theorem of A. Kupiainen, R. Rhodes and V. Vargas (Annals of Mathematics, 2020) that the three-point structure constants of Liouville conformal field theory on the Riemann sphere are given by the DOZZ formula of Dorn–Otto and Zamolodchikov–Zamolodchikov. The structure constants are defined probabilistically: for 0 0 and charges satisfying the extended Seiberg bounds, C_gamma(alpha_1, alpha_2, alpha_3) = 2 mu^(-s) gamma^(-1) Gamma(s) E[rho^(-s)], where rho integrates explicit power weights against the Gaussian multiplicative chaos of the Gaussian free…
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