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 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.
Highlights
As a generalization of the Yang-Baxter sigma model description, one may consider classical Yang-Baxter equation (CYBE) rather than mCYBE
Abelian twists of AdS5 are investigated. These results provide a support for the gravity/CYBE correspondence proposed in arXiv:1404.1838
We derive the gravity duals of noncommutative (NC) gauge theories [36, 37] from the Yang-Baxter sigma model description of the AdS5 × S5 superstring with classical r-matrices
Summary
According to the construction of the deformed string action, one may expect the correspondence between integrable deformations of AdS5 × S5 and classical r-matrices, called the gravity/CYBE correspondence [35]. To study along this direction, it would be valuable to classify some typical class of skew-symmetric solutions of CYBE. The first class is classical r-matrices of Jordanian type, rJor = Eij ∧ (Eii − Ejj) − 2. We will show that classical r-matrices of abelian Jordanian type correspond to the gravity duals of NC gauge theories [36, 37]
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