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We derive the gravity duals of noncommutative gauge theories from theYang-Baxter sigma model description of the AdS_5xS^5 superstring with classicalr-matrices. The corresponding classical r-matrices are 1) solutions of theclassical Yang-Baxter equation (CYBE), 2) skew-symmetric, 3) nilpotent and 4)abelian. Hence these should be called abelian Jordanian deformations. As aresult, the gravity duals are shown to be integrable deformations of AdS_5xS^5.Then, abelian twists of AdS_5 are also investigated. These results provide asupport for the gravity/CYBE correspondence proposed in arXiv:1404.1838.

Integrability of classical strings dual for noncommutative gauge theories