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

A bstract We consider γ-deformations of the AdS 5 ×S 5 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 AdS 5 ×S 5 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.