Related papers: Quantum properties and generalised T-duality of th…

We study a class of $\mathcal{E}$-models, referred to as Euclidean $\mathcal{E}$-models, in which the operator $\mathcal{E}$ acting on the Drinfeld double squares to minus the identity rather than to the identity. This modification leads to…

In this work, based on the Petrov-Diakonov representation of the Wilson loop average W in the SU(2) Yang-Mills theory, together with the Cho-Fadeev-Niemi decomposition, we present a natural framework to discuss possible ideas underlying…

We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the $q\to\infty$ limit of the q-deformed WZW model and the understanding of its…

We formulate Poisson-Lie T-duality in a path-integral manner that allows us to analyze the quantum corrections. Using the path-integral, we rederive the most general form of a Poisson-Lie dualizeable background and the generalized Buscher…

In this paper, we explore a new class of integrable sigma models, which we refer to as the "dual regime" of Yang-Baxter (YB) deformed $\mathrm{O}(2N)$ sigma models. This dual regime manifests itself in the conformal perturbation approach.…

We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras,…

We consider the $T\bar{T}$ deformation of two dimensional Yang--Mills theory on general curved backgrounds. We compute the deformed partition function through an integral transformation over frame fields weighted by a Gaussian kernel. We…

We prove the integrability of the Yang-Baxter $\si$-model which is the Poisson-Lie deformation of the principal chiral model. We find also an explicit one-to-one map transforming every solution of the principal chiral model into a solution…

We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…

It turns out that many integrable $\sigma$-models on group manifolds belong to the class of the so-called ${ \mathcal E}$-models which are relevant in the context of the Poisson-Lie T-duality. We show that this is the case also for the…

The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality--shift--T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in…

This thesis deals with a class of integrable field theories called models with twist function. The main examples of such models are integrable non-linear sigma models, such as the Principal Chiral Model, and their deformations. A first…

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct…

In superdimension $(2|2)$ there are only three non-Abelian Lie superalgebras admitting non-degenerate ad-invariant supersymmetric metric, the well-known Lie superalgebra $gl(1|1)$, and two more, $({\C}^3 + \A)$ and $({\C}_0^5 +{\A})$. After…

q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide…

Starting with a four-dimensional gauge theory approach to rational, elliptic, and trigonometric solutions of the Yang-Baxter equation, we determine the corresponding quantum group deformations to all orders in $\hbar$ by deducing their RTT…

A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space.…

Poisson-Lie dualising the eta deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated lambda deformed model. In this paper we investigate…

Poisson-Lie T-duality in N=2 superconformal WZNW models on the real Lie groups is considered. It is shown that Poisson-Lie T-duality is governed by the complexifications of the corresponding real groups endowed with Semenov-Tian-Shansky…

Using the concept of Jacobi-Lie group and Jacobi-Lie bialgebra, we generalize the definition of Poisson-Lie symmetry to Jacobi-Lie symmetry. In this regard, we generalize the concept of Poisson-Lie T-duality to Jacobi-Lie T-duality and…