This review provides an introduction to non-geometric backgrounds in string theory. Starting
from a discussion of T-duality, geometric and non-geometric torus-fibrations are reviewed …

The standard notion of the non-Abelian duality in string theory is generalized to the class of
σ-models admitting a Poisson-Lie-like 3ymmetry. Such σ-models can be associated with …

In these lectures a general introduction to T-duality is given. In the abelian case the
approaches of Buscher, and Roc̆ek and Verlinde are reviewed. Buscher's prescription for …

The Wigner phase-space distribution function provides the basis for Moyal's deformation
quantization alternative to the more conventional Hilbert space and path integral …

We show how to implement T-duality along non-abelian isometries in backgrounds with non-
vanishing Ramond fields. When the dimension of the isometry group is odd (even) the …

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 σ-models in a pair related by Poisson-Lie T …

A description of dual non-Abelian duality is given, based on the notion of the Drinfeld
double. The presentation basically follows the original paper\cite {KS2}, written in …

We construct the actions of a very broad family of 2d integrable $\sigma $-models. Our
starting point is a universal 2d action obtained in [arxiv: 2008.01829] using the framework of …

We discuss 2 d duality transformations in the classical AdS 5× S 5 superstring and their
effect on the integrable structure. T-duality along four directions in the Poincaré …

A bstract We show that the approaches to integrable systems via 4d Chern-Simons theory
and via symmetry reductions of the anti-self-dual Yang-Mills equations are closely related, at …