Related papers: On classical q-deformations of integrable sigma-mo…
We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…
Based on work done by Bonechi, Cattaneo, Felder and Zabzine on Poisson sigma models, we formally show that Kontsevich's star product can be obtained from the twisted convolution algebra of the geometric quantization of a Lie 2-groupoid, one…
The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2,R) coalgebra symmetry. By using the properties induced by such a coalgebra…
We construct a Lax pair with spectral parameter for a two-parameter doubly Poisson-Lie deformation of the principal chiral model.
We discuss the deformed sigma-model that arises when considering four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry…
We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of…
We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T^{1,1}, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein…
A three-parameter integrable deformation of $\mathbb{Z}_4$ permutation supercosets is constructed. These supercosets are of the form $ {\widehat{F}} / {F_0}$ where $F_0$ is the bosonic diagonal subgroup of the product supergroup…
We find the novel class of the supersymmetric deformation of the $\mathbb{CP}^{1}$ $\sigma$-model and its equivalence with the generalised chiral Gross-Neveu. This construction allows the use of field-theoretic techniques and particularly…
I investigate the Poisson-sigma model on the classical and quantum level. First I show how the interaction can be obtained by a deformation of the classical master equation of an Abelian BF theory in two dimensions. On the classical level…
An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…
We present a general construction of integrable degenerate $\mathcal E$-models on a 2d manifold $\Sigma$ using the formalism of Costello and Yamazaki based on 4d Chern-Simons theory on $\Sigma \times \mathbb{C}P^1$. We begin with a…
Deformation spaces Hom($\pi$,G)/G of representations of the fundamental group $\pi$ of a surface $\Sigma$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_\Sigma$, preserving a Poisson structure. When $G$ is compact,…
We study the effective action for the integrable $\lambda$-deformation of the $G_{k_1} \times G_{k_2}/G_{k_1+k_2}$ coset CFTs. For unequal levels theses models do not fall into the general discussion of $\lambda$-deformations of CFTs…
We introduce the notion of a classical dihedral affine Gaudin model, associated with an untwisted affine Kac-Moody algebra $\widetilde{\mathfrak{g}}$ equipped with an action of the dihedral group $D_{2T}$, $T \geq 1$ through (anti-)linear…
In this short proceedings we discuss some of the results obtained in [1]. Integrable deformations enlarge the landscape and understanding of integrable models and its algebraic structures like quantum groups. In this short proceedings, we…
The homogeneous Yang-Baxter deformation is part of a larger web of integrable deformations and dualities that recently have been studied with motivations in integrable $\sigma$-models, solution-generating techniques in supergravity and…
We derive a novel two-field four-dimensional integrable field theory (IFT) from 6d holomorphic Chern-Simons theory on twistor space. The four-dimensional IFT depends on a skew-symmetric linear operator acting on a Lie algebra, and when this…
A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky-Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the…
We explore two distinct methods to introduce integrable defects in a family of integrable sigma-models known as Yang-Baxter models. The first method invokes a modified monodromy matrix encoding an integrable defect separating two integrable…