2017/03/31 by S. Lacroix, Sylvain Lacroix, M. Magro +3 · 1 citation
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Central charge #Chiral model #Current algebra #Hamiltonian (control theory) #Homotopy and Cohomology in Algebraic Topology #Integrable system #Involution (esoterism) #Lie algebra #Nonlinear Waves and Solitons #Twist #hep-th
paper · pdf · doi:10.1007/jhep09(2017)117
published as JHEP 1709 (2017) 117 · 67 pages, published version
openalex created_date 2017/03/16 · openalex publication_date 2017/09/01 · arxiv created 2017/10/17 · arxiv updated 2017/10/18 · openalex updated_date 2026/08/06
Integrable σ-models, such as the principal chiral model, ℤT -coset models for T∈ ℤ≥ 2 and their various integrable deformations, are examples of non-ultralocal integrable field theories described by r/s-systems with twist function. In this general setting, and when the Lie algebra \mathfrakg underlying the r/s-system is of classical type, we construct an infinite algebra of local conserved charges in involution, extending the approach of Evans, Hassan, MacKay and Mountain developed for the principal chiral model and symmetric space σ-model. In the present context, the local charges are attached to certain ‘regular’ zeros of the twist function and have increasing degrees related to the exponents of the untwisted affine Kac-Moody algebra \widehat\mathfrakg associated with \mathfrakg . The Hamiltonian flows of these charges are shown to generate an infinite hierarchy of compatible integrable equations.