  We derive the gravity duals of noncommutative gauge theories from the
Yang-Baxter sigma model description of the AdS_5xS^5 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 AdS_5xS^5.
Then, abelian twists of AdS_5 are also investigated. These results provide a
support for the gravity/CYBE correspondence proposed in arXiv:1404.1838.
