Abstract
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
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