Liouville field theory coupled to a critical Ising model: non-perturbative analysis, duality and applications Original Research Article

Two different kinds of interactions between a Zn-parafermionic and a Liouville field theory are considered. For generic values of n, the effective central charges describing the UV behavior of both models are calculated in the Neveu–Schwarz sector. For n=2 exact vacuum expectation values of primary fields of the Liouville field theory, as well as the first descendent fields are proposed. For n=1, known results for sinh-Gordon and Bullough–Dodd models are recovered whereas for n=2, exact results for these two integrable coupled Ising–Liouville models are shown to exchange under a weak–strong coupling duality relation. In particular, exact relations between the parameters in the actions and the mass of the particles are obtained. At specific imaginary values of the coupling and n=2, we use previous results to obtain exact information about: (a) integrable coupled models like Ising–Mp/p′, homogeneous sine-Gordon model SU(3)2 or the Ising–XY model, (b) Neveu–Schwarz sector of the Φ13 integrable perturbation of N=1 supersymmetric minimal models. Several non-perturbative checks are done, which support the exact results.