2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225508There exists an intriguing relation between genus zero correlation functions in the H^+_3 WZNW model and in Liouville field theory. We provide a path integral derivation of the correspondence and then use our new approach to generalize the relation to surfaces of arbitrary genus g. In particular we determine the correlation functions of N primary fields in the WZNW model explicitly through Liouville correlators with N+2g-2 additional insertions of certain degenerate fields. The paper concludes with a list of interesting further extensions and a few comments on the relation to the geometric Langlands program.33 pages, no figure, minor changes, several equations correctedHigh Energy Physics - Theorytext