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Integrability of classical strings dual for noncommutative gauge theories. (English) Zbl 1333.81262
Summary: We derive the gravity duals of noncommutative gauge theories from the Yang-Baxter sigma model description of the \(\mathrm{AdS}_5\times S^5\) 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 \(\mathrm{AdS}_5\times S^5\). Then, abelian twists of \(\mathrm{AdS}_5\) are also investigated. These results provide a support for the gravity/CYBE correspondence proposed in [the authors, ibid. 2014, No. 6, Paper No. 135, 15 p. (2014; Zbl 1333.83196)].

MSC:
81T13 Yang-Mills and other gauge theories in quantum field theory
81R60 Noncommutative geometry in quantum theory
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