In this pedagogical review we introduce systematic approaches to deforming integrable two-
dimensional sigma models. We use the integrable principal chiral model and the conformal …

These lecture notes concern the semi-holomorphic 4D Chern–Simons theory and its
applications to classical integrable field theories in 2D and in particular integrable sigma …

We show that the so-called λ deformed σ-model as well as the η deformed one belong to a
class of the E-models introduced in the context of the Poisson–Lie-T-duality. The λ and η …

A bstract The worldsheet theories that describe Poisson-Lie T-dualisable σ-models on group
manifolds as well as integrable η, λ and β-deformations provide examples of ℰ-models …

We describe a unifying framework for the systematic construction of integrable deformations
of integrable σ-models within the Hamiltonian formalism. It applies equally to both the'Yang …

In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-
dimensional variant of Chern–Simons theory, we derive a simple and unifying two …

We introduce the notion of a classical dihedral affine Gaudin model, associated with an
untwisted affine Kac–Moody algebra equipped with an action of the dihedral group, through …

We construct a two-parameter deformation of the Metsaev–Tseytlin action for supercosets
with isometry group of the form G ˆ× G ˆ. The resulting action is classically integrable and is …

A bstract We explain how to obtain new classical integrable field theories by assembling two
affine Gaudin models into a single one. We show that the resulting affine Gaudin model …

A bstract We examine integrable λ-deformations of SO (n+ 1)/SO (n) coset CFTs and their
analytic continuations. We provide an interpretation of the deformation as a squashing of the …