Integrability, Duality and Sigma Models

V.A. Fateev (1, 2) , Alexey V. Litvinov (2, 3)

1 L2C - Laboratoire Charles Coulomb
2 L.D. Landau Institute for Theoretical Physics of RAS
3 IITP - Kharkevich Institute for Information Transmission Problems

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 ansatz 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.

Mots clés: Renormalization group; Duality; Nonlocal; Sigma model: O(N); Charge: screening; Field theory: integrability; Field theory: conformal; Sigma Models; Integrable Field Theories; Conformal Field Theory; Scattering; Algebra: Lie

Domaines: Physique des Hautes Energies - Théorie [hep-th]

V.A. Fateev, Alexey V. Litvinov. Integrability, Duality and Sigma Models. Journal of High Energy Physics, 2018, 11, pp.204. ⟨10.1007/JHEP11(2018)204⟩. ⟨hal-01774013⟩