Liouville field theory coupled to a critical Ising model: Non-perturbative analysis, duality and applications

Abstract

Two different kinds of interactions between a $Z_n$-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-${\mathcal{M}}_{p/p^{\prime }}$, homogeneous sine-Gordon model $SU(3{)}_2$ or the Ising-XY model; (b) Neveu-Schwarz sector of the ${\Phi }_{13}$ integrable perturbation of N=1 supersymmetric minimal models. Several non-perturbative checks are done, which support the exact results.

29 pages, 1 fig., LaTeX file with epsfig, amssymb, 3 references added. To appear in Nucl. Phys. B

References in corpus (1)

• Expectation values of descendent fields in the Bullough-Dodd model and related perturbed conformal field theories

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