Abstract
Based on the formulation of Yang-Baxter sigma models developed by Klimcik and Delduc-Magro-Vicedo, we explain that various deformations of type IIB superstring on AdS5 × S5 can be charactered by classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The relation may be referred to as the gravity/CYBE correspondence. We present non-trivial examples of the correspondence including Lunin-Maldacena backgrounds for β-deformations of the N = 4 super Yang-Mills theory and the gravity duals for non-commutative gauge theories. We also discuss non-integrable backgrounds such as AdS5 × T1,1 as a generalization.
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