We study a GKP-like classical string solution on a q-deformed AdS 5 ×S 5 background and argue the spacetime structure by using it as a probe. The solution cannot stretch beyond the singularity surface and this result may suggest that the holographic relation is realized inside the singularity surface. This observation leads us to introduce a new coordinate system which describes the spacetime only inside the singularity surface. With the new coordinate system, we study minimal surfaces and derive a deformed Neumann-Rosochatius system with a rigid string ansatz.
A multi-parameter integrable deformation of the principal chiral model is presented. The Yang-Baxter and bi-Yang-Baxter σ-models, the principal chiral model plus a Wess-Zumino term and the TsT transformation of the principal chiral model are all recovered when the appropriate deformation parameters vanish. When the Lie group is SU(2), we show that this four-parameter integrable deformation of the SU(2) principal chiral model corresponds to the Lukyanov model.
A three-parameter integrable deformation of Z 4 permutation supercosets is constructed.These supercosets are of the form F /F 0 where F 0 is the bosonic diagonal subgroup of the product supergroup F = G × G. They include the AdS 3 × S 3 and AdS 3 × S 3 × S 3 supercosets. This deformation encompasses both the bi-Yang-Baxter deformation of the semi-symmetric space σ-model on Z 4 permutation supercosets and the mixed flux model.Truncating the action at the bosonic level, we show that one recovers the bi-Yang-Baxter deformation of the principal chiral model plus Wess-Zumino term. in [6] rely on the deformation being governed by a solution of the modified classical Yang-Baxter equation. The two-parameter bi-Yang-Baxter deformation of the principal chiral model was introduced in [5] and shown to be integrable in [7,8]. As demonstrated in [9], the bi-Yang-Baxter deformation of the SU (2) principal chiral model is equivalent to the two-parameter deformation of S 3 found in [10]. In [6] the Yang-Baxter deformation of the symmetric space σ-model was constructed and shown to be integrable. For symmetric spaces that take the form of Z 2 permutation cosets (1.2), the deformed model is equivalent to a particular one-parameter model contained within the bi-Yang-Baxter deformation of the principal chiral model on F 0 .Adding the standard topological Wess-Zumino term [11][12][13] to the principal chiral model is well-known to preserve its classical integrability. Up to the expected quantization of the level, the resulting model interpolates between the principal chiral and conformal Wess-Zumino-Witten models. Generalising the SU (2) construction of [14,15], the Yang-Baxter deformation of the principal chiral model plus Wess-Zumino term for general Lie groups was derived in [16]. In order to construct this deformation it was assumed that the solution of the modified classical Yang-Baxter deformation governing the deformation cubes to its negative. This assumption is natural since it is satisfied by the standard Drinfel'd-Jimbo R-matrix for a non-split real form of a semi-simple Lie algebra [17][18][19]. In this article we will continue to focus on deformations governed by such R-matrices.By allowing for an antisymmetric term in the action, the two-parameter deformation of [10] was generalised to an integrable four-parameter deformation of S 3 in [2]. Observing that this model also contains the TsT transformation of the SU (2) Wess-Zumino-Witten model [20, 21], it was proposed in [9] that the four-parameter model should be understood as the combined bi-Yang-Baxter deformation and TsT transformation of the σ-model on S 3 plus Wess-Zumino term. The bi-Yang-Baxter deformation of the principal chiral model plus Wess-Zumino term was constructed in [1]. Applying a TsT transformation in the directions of the Cartan subalgebra, which is associated with adding a compatible abelian solution of the classical Yang-Baxter equation [22-29] to the Drinfel'd-Jimbo R-matrix, and considering the SU (2) case it was shown that this model indeed genera...
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