Assembling integrable σ-models as affine Gaudin models

• Published in: The journal of high energy physics 2019-06, Vol.2019 (6), p.1-88, Article 17
• Main Authors: Delduc, F., Lacroix, S., Magro, M., Vicedo, B.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Decoupling; Deformation mechanisms; Elementary Particles; High energy physics; High Energy Physics - Theory; Integrable Field Theories; Lie groups; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Sigma Models; String Theory
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP06(2019)017

A bstract We explain how to obtain new classical integrable field theories by assembling two affine Gaudin models into a single one. We show that the resulting affine Gaudin model depends on a parameter γ in such a way that the limit γ → 0 corresponds to the decoupling limit. Simple conditions ensuring Lorentz invariance are also presented. A first application of this method for σ -models leads to the action announced in [ 1 ] and which couples an arbitrary number N of principal chiral model fields on the same Lie group, each with a Wess-Zumino term. The affine Gaudin model descriptions of various integrable σ -models that can be used as elementary building blocks in the assembling construction are then given. This is in particular used in a second application of the method which consists in assembling N − 1 copies of the principal chiral model each with a Wess-Zumino term and one homogeneous Yang-Baxter deformation of the principal chiral model.