Integrability, Duality and Sigma Models

Abstract

We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFT's possess perturbations which define integrable QFT's. We establish that these QFT's have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the $S-$matrix of this QFT tends to the scattering matrix of the $O(N)$ sigma model. The perturbation theory, Bethe anzatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFT's are dual to integrable deformation of $O(N)$ sigma-models.

References in corpus (1)

• Multipoint correlation functions in Liouville field theory and minimal Liouville gravity

Cited by in corpus (10)

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• Dual description of $\eta$-deformed OSP sigma models
• On some integrable deformations of the Wess-Zumino-Witten model
• Integrable sigma models on Riemann surfaces
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• Integrable $\mathfrak{gl}(n|n)$ Toda field theory and its sigma-model dual
• On dual regime in Yang-Baxter deformed $\mathrm{O}(2N)$ sigma models