Related papers: On classical q-deformations of integrable sigma-mo…
Dimensional reduction of gravity theories to $D=2$ along commuting Killing isometries is well-known to be classically integrable. The resulting system typically features a coset $\sigma$-model coupled to a dilaton and a scale factor of the…
We introduce the $\mathbb{Z}_N$-twisted trigonometric sigma models, a new class of integrable deformations of the principal chiral model. Starting from 4d Chern-Simons theory on a cylinder, the models are constructed by introducing a…
Yang-Baxter string sigma-models provide a systematic way to deform coset geometries, such as $AdS_p \times S^p$, while retaining the $\sigma$-model integrability. It has been shown that the Yang-Baxter deformation in target space is simply…
The notion of quantum algebras is merged with that of Lie systems in order to establish a new formalism called Poisson-Hopf algebra deformations of Lie systems. The procedure can be naturally applied to Lie systems endowed with a symplectic…
It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion…
We introduce a new elliptic integrable $\sigma$-model in the form of a two-parameter deformation of the Principal Chiral Model on the group $\text{SL}_{\mathbb{R}}(N)$, generalising a construction of Cherednik for $N=2$ (up to reality…
Using the general method presented by Mohammedi \cite{NM} for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex…
Yang-Baxter sigma models, proposed by Klimcik and Delduc-Magro-Vicedo, have been recognized as a powerful framework for studying integrable deformations of two-dimensional non-linear sigma models. In this short article, as an important…
Integrable deformations of a class of Rikitake dynamical systems are constructed by deforming their underlying Lie-Poisson Hamiltonian structures, which are considered linearizations of Poisson--Lie structures on certain (dual) Lie groups.…
A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In…
The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with…
We review and pursue further the study of constrained realisations of affine Gaudin models, which form a large class of two-dimensional integrable field theories with gauge symmetries. In particular, we develop a systematic gauging…
An operator deformed quantum algebra is discovered exploiting the quantum Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along with its $q \to 1$ limit appear to be the most general Yang-Baxter algebra underlying…
Based on a recently developed procedure to construct Poisson-Hopf deformations of Lie-Hamilton systems, a novel unified approach to nonequivalent deformations of Lie-Hamilton systems on the real plane with a Vessiot-Guldberg Lie algebra…
This study introduces a new unified structural framework for orbifold sigma models that incorporates twisted sectors, singularities, and smooth regions into a single algebraic object. Traditional approaches to orbifold theories often treat…
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti--self--dual Yang--Mills equations with a gauge group Diff$(S^1)$.
We construct a generalisation of the $\lambda$-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup $F$ of the full symmetry group $G$. We find that demanding Lax integrability imposes a crucial restriction,…
We define integrability preserving Yang-Baxter deformations of symmetric space sigma models with non-semi-simple symmetry group, in particular the flat space string, using only the essential structures of a symmetric space sigma model. For…
Integrable $\sigma$-models, such as the principal chiral model, ${\mathbb{Z}}_T$-coset models for $T \in {\mathbb{Z}}_{\geq 2}$ and their various integrable deformations, are examples of non-ultralocal integrable field theories described by…
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…