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

TL;DR

This paper investigates the non-perturbative properties, dualities, and applications of models coupling Liouville field theory with a critical Ising or parafermionic model, revealing exact results and relations between parameters.

Contribution

It introduces new exact results and duality relations for coupled Liouville and parafermionic models, extending understanding of their UV behavior and integrable structures.

Findings

Exact vacuum expectation values for n=2 models.

Duality relations exchanging weak and strong coupling.

Connections to known integrable models like Sinh-Gordon and Bullough-Dodd.

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-${\cal M}_{p/p'}$, 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.