Integrability of classical strings dual for noncommutative gauge theories

We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the AdS₅ × S⁵ superstring with classical r-matrices. The corresponding classical r-matrices are 1) solutions of the classical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4) abelian. Hence these should be called abelian Jordanian deformations. As a result, the gravity duals are shown to be integrable deformations of AdS₅ × S⁵. Then, abelian twists of AdS₅ are also investigated. These results provide a support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.