We consider Jordanian deformations of the AdS 5 ×S 5 superstring action. These deformations correspond to non-standard q-deformations. In particular, it is possible to perform a partial deformation, for example, of the AdS 5 part only, or of the S 5 part only. Then the classical action and the Lax pair are constructed with a linear, twisted and extended R operator. It is shown that the action preserves the κ-symmetry.

We consider a Jordanian deformation of the AdS_5xS^5 superstring action by taking a simple R-operator which satisfies the classical Yang-Baxter equation. The metric and NS-NS two-form are explicitly derived with a coordinate system. Only the AdS part is deformed and the resulting geometry contains the 3D Schrodinger spacetime as a subspace. Then we present the full solution in type IIB supergravity by determining the other field components. In particular, the dilaton is constant and a R-R three-form field strength is turned on. The symmetry of the solution is [SL(2,R)xU(1)^2] x [SU(3)xU(1)] and contains an anisotropic scale symmetry.Comment: 29 pages, no figure, LaTeX, typos corrected, references added, further clarification adde

We show that SU(2)_L Yangian and q-deformed SU(2)_R symmetries are realized in a two-dimensional sigma model defined on a three-dimensional squashed sphere. These symmetries enable us to develop the two descriptions to describe its classical dynamics, 1) rational and 2) trigonometric descriptions. The former 1) is based on the SU(2)_L symmetry and the latter 2) comes from the broken SU(2)_R symmetry. Each of the Lax pairs constructed in both ways leads to the same equations of motion. The two descriptions are related one another through a non-local map.Comment: 12 pages, LaTeX, typos corrected and references added, further clarification adde

We discuss a hidden symmetry of a two-dimensional sigma model on a squashed S^3. The SU(2) current can be improved so that it can be regarded as a flat connection. Then we can obtain an infinite number of conserved non-local charges and show the Yangian algebra by directly checking the Serre relation. This symmetry is also deduced from the coset structure of the squashed sphere. The same argument is applicable to the warped AdS_3 spaces via double Wick rotations.Comment: 11 pages, 1 figure, typos corrected, references adde

We introduce a deformation of the Wess-Zumino-Novikov-Witten model with threedimensional squashed sphere target space. We show how with an appropriate choice of Wess-Zumino and boundary terms it is possible to construct an infinite family of conserved charges realizing an SU(2) Yangian. Finally we discuss the running of the squashing parameter under renormalization group flow.