Lunin-Maldacena backgrounds from the classical Yang-Baxter equation - Towards the gravity/CYBE correspondence

We consider γ-deformations of the AdS₅×S⁵ superstring as Yang-Baxter sigma models with classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). An essential point is that the classical r-matrices are composed of Cartan generators only and then generate abelian twists. We present examples of the r-matrices that lead to real γ-deformations of the AdS₅×S⁵ superstring. Finally we discuss a possible classification of integrable deformations and the corresponding gravity solution in terms of solutions of CYBE. This classification may be called the gravity/CYBE correspondence.