New integrable coset sigma models

Abstract

By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of $N$ copies of a Lie group over some diagonal subgroup and they depend on $3N-2$ free parameters. For $N=1$ the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the $N=2$ case and show that it admits a remarkably simple form in terms of the classical $\mathcal{R}$-matrix underlying the integrability of these models. We conjecture that a similar form of the Lagrangian holds for arbitrary $N$. Specifying our general construction to the case of $SU(2)$ and $N=2$, and eliminating one of the parameters, we find a new three-parametric integrable model with the manifold $T^{1,1}$ as its target space. We further comment on the connection of our results with those existing in the literature.

arXiv comment43 pages. v2: published version, minor changes and references added

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Cited by in corpus (13)

• Integrable Deformations of Sigma Models
• 4-dimensional Chern-Simons theory and integrable field theories
• Chaotic string dynamics in deformed $T^{1,1}$
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• Integrable deformed $T^{1,1}$ sigma models from 4D Chern-Simons theory
• The Magic Renormalisability of Affine Gaudin Models
• Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex
• On a class of conformal $\mathcal{E}$-models and their chiral Poisson algebras
• 3-dimensional mixed BF theory and Hitchin's integrable system
• Analytic (non)integrability of Arutyunov-Bassi-Lacroix model
• Chaotic string dynamics in Bosonic $\eta$-deformed $Ad{S}_5\times T^{1,1}$ background
• Bosonic $\eta$-deformations of Non-integrable Backgrounds