Langlands duality in Liouville-H_3^+ WZNW correspondence

We show a physical realization of the Langlands duality in correlation functions of H_3^+ WZNW model. We derive a dual version of the Stoyanovky-Riabult-Teschner (SRT) formula that relates the correlation function of the H_3^+ WZNW and the dual Liouville theory to investigate the level duality k-2 o (k-2)^{-1} in the WZNW correlation functions. Then, we show that such a dual version of the H_3^+ - Liouville relation can be interpreted as a particular case of a biparametric family of non-rational CFTs based on the Liouville correlation functions, which was recently proposed by Ribault. We study symmetries of these new non-rational CFTs and compute correlation functions explicitly by using the free field realization to see how a generalized Langlands duality manifests itself in this framework. Finally, we suggest an interpretation of the SRT formula as realizing the Drinfeld-Sokolov Hamiltonian reduction. Again, the Hamiltonian reduction reveals the Langlands duality in the H_3^+ WZNW model. Our new identity for the correlation functions of H_3^+ WZNW model may yield a first step to understand quantum geometric Langlands correspondence yet to be formulated mathematically. Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Nakayama, Yu. University of California; Estados UnidosFil: Nicolas, Lorena. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentin