Related papers: Poisson-Lie T-Duality beyond the classical level a…
We investigate Poisson-Lie duals of the $\eta$-deformed $\mathrm{AdS}_2 \times \mathrm{S}^2 \times \mathrm{T}^6$ superstring. The $\eta$-deformed background satisfies a generalisation of the type II supergravity equations. We discuss three…
The supersymmetric generalization of Pisson-Lie T-duality in N=2 superconformal WZNW models on the compact groups is considered. It is shown that the role of Drinfeld's doubles play the complexifications of the corresponding compact groups.…
Covariance of the one-loop renormalization group equations with respect to Poisson-Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson-Lie sigma models with truncated matrices…
We perform a systematic study of the one-loop renormalizability of all Poisson-Lie T-dualizable $\si$-models with two-dimensional targets. We show that whatever Drinfeld double and whatever matrix of coupling constants we consider the…
We initiate the study of the interplay between T-duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T-duality commutes with the $T \overline{T}$ deformation, which can be…
We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. As an…
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized…
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincare duality), and a similar formulation is given for…
Poisson-Lie target space duality is a framework where duality transformations are properly defined. In this letter we investigate the pair of sigma models defined by the double SO(3,1) in the Iwasawa decomposition.
We describe topological T-duality and Poisson-Lie T-duality in terms of QP (differential graded symplectic) manifolds and their canonical transformations. Duality is mediated by a QP-manifold on doubled non-abelian "correspondence" space,…
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…
A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $\sigma$-models related by Poisson-Lie T-duality. Remarkably, the action contains…
By calculating inequivalent classical r-matrices for the $gl(2,\mathbb{R})$ Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE)), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the…
We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group…
We review aspects of Poisson-Lie T-duality which we explicitly formulate as a canonical transformation on the world-sheet. Extensions of previous work on T-duality in relation to supersymmetry are also discussed. (Contribution to the…
We describe non-Abelian T-dualities for $\mathcal{N} = 2$ two dimensional gauged linear sigma model (GLSM). We start with the case of left and right $(2, 2)$ supersymmetry (SUSY), $U(1)$ gauge group, and global non-Abelian symmetries. Our…
In this study, we proceed to investigate the Thurston geometries from the point of view of their Poisson-Lie (PL) T-dualizability. First of all, we find all subalgebras of Killing vectors that generate group of isometries acting freely and…
The quantum duality principle is used to obtain explicitly the Poisson analogue of the kappa-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson-Lie structure on the dual solvable Lie group. The construction is fully…
We study a connection between duality and topological field theories. First, 2d Kramers-Wannier duality is formulated as a simple 3d topological claim (more or less Poincar\'e duality), and a similar formulation is given for…
We use a generalized Ricci tensor, defined for generalized metrics in Courant algebroids, to show that Poisson-Lie T-duality is compatible with the 1-loop renormalization group.