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We introduce and study conformal field theories specified by $W-$algebras commuting with certain set of screening charges. These CFTs possess perturbations which define integrable QFTs. We establish that these QFTs have local and non-local Integrals of Motion and admit the perturbation theory in the weak coupling region. We construct factorized scattering theory which is consistent with non-local Integrals of Motion and perturbation theory. In the strong coupling limit the $S-$matrix of this QFT tends to the scattering matrix of the $O(N)$ sigma model. The perturbation theory, Bethe anzatz technique, renormalization group approach and methods of conformal field theory are applied to show, that the constructed QFTs are dual to integrable deformation of $O(N)$ sigma-models.
We consider several classes of $sigma$-models (on groups and symmetric spaces, $eta$-models, $lambda$-models) with local couplings that may depend on the 2d coordinates, e.g. on time $tau$. We observe that (i) starting with a classically integrable 2
We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any s
The $O(d,d)$ invariant worldsheet theory for bosonic string theory with $d$ abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of mo
For the rational quantum Calogero systems of type $A_1{oplus}A_2$, $AD_3$ and $BC_3$, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra `od
Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure of supersy