We show how so-called Yang-Baxter (YB) deformations of sigma models, based on an R-matrix solving the classical Yang-Baxter equation (CYBE), give rise to marginal current-current deformations when applied to the Wess-Zumino-Witten (WZW) model. For non-compact groups these marginal deformations are more general than the ones usually considered, since they can involve a non-Abelian current subalgebra. We classify such deformations of the AdS(3) x S-3 string.

We perform non-abelian T-duality for a generic Green-Schwarz string with respect to an isometry (super)group G, and we derive the transformation rules for the supergravity background fields. Specializing to G bosonic, or G fermionic but abelian, our results reproduce those available in the literature. We discuss also continuous deformations of the T-dual models, obtained by adding a closed B-field before the dualization. This idea can also be used to generate deformations of the original (un-dualized) model, when the 2-cocycle identified from the closed B is invertible. The latter construction is the natural generalization of the so-called Yang-Baxter deformations, based on solutions of the classical Yang-Baxter equation on the Lie algebra of G and originally constructed for group manifolds and (super)coset sigma models. We find that the deformed metric and B-field are obtained through a generalization of the map between open and closed strings that was used also in the discussion by Seiberg and Witten of non-commutative field theories. When applied to integrable sigma models these deformations preserve the integrability.

We consider the exact R-matrix of AdS(3)/CFT2, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds AdS(3) x S-3 x T-4 and AdS(3) x S-3 x S-3 x S-1 with pure Ramond-Ramond fluxes. We show that R is invariant under a deformed boost symmetry, for which we write an explicit exact coproduct, i.e. its action on two-particle states. When we include the boost, the symmetries of the R-matrix close into a q-Poincare superalgebra. Our findings suggest that the recently discovered boost invariance in AdS(5)/CFT4 may be a common feature of AdS/CFT systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the AdS(3)/CFT2 classical r-matrix.

We consider the exact S-matrix governing the planar spectral problem for strings on AdS(5) x S-5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel boost symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu(2 vertical bar 2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincare supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincare symmetry, by contraction of the quantum affine algebra U-q((sl(2)) over cap) in Drinfeld's second realisation.

We elaborate on the class of deformed T-dual (DTD) models obtained by first adding a topological term to the action of a supercoset sigma model and then performing (non-abelian) T-duality on a subalgebra (g) over tilde of the superisometry algebra. These models inherit the classical integrability of the parent one, and they include as special cases the socalled homogeneous Yang-Baxter sigma models as well as their non-abelian T-duals. Many properties of DTD models have simple algebraic interpretations. For example we show that their (non-abelian) T-duals - including certain deformations - are again in the same class, where (g) over tilde gets enlarged or shrinks by adding or removing generators corresponding to the dualised isometries. Moreover, we show that Weyl invariance of these models is equivalent to (g) over tilde being unimodular; when this property is not satisfied one can always remove one generator to obtain a unimodular (g) over tilde, which is equivalent to (formal) T-duality. We also work out the target space super fields and, as a by-product, we prove the conjectured transformation law for Ramond-Ramond (RR) fields under bosonic non-abelian T-duality of supercosets, generalising it to cases involving also fermionic T-dualities.