Hoare, Ben; van Tongeren, Stijn J. On Jordanian deformations of \(\mathrm{AdS}_{5}\) and supergravity. (English) Zbl 1352.81050 J. Phys. A, Math. Theor. 49, No. 43, Article ID 434006, 22 p. (2016). Summary: We consider various homogeneous Yang-Baxter deformations of the \({\mathrm{AdS}}_{5}\times {\mathrm{S}}^{5}\) superstring that can be obtained from the \(\eta\)-deformed superstring and related models by singular boosts. The Jordanian deformations we obtain in this way behave similarly to the \(\eta\)-deformed model with regard to supergravity: \(T\) dualizing the classical sigma model it is possible to find corresponding solutions of supergravity, which, however, have dilatons that prevent \(T\) dualizing back. Hence the backgrounds of these Jordanian deformations are not solutions of supergravity. Still, they do satisfy a set of recently found modified supergravity equations which implies that the corresponding sigma models are scale invariant. The abelian models that we obtain by singular boosts do directly correspond to solutions of supergravity. In addition to our main results we consider contraction limits of our main example, which do correspond to supergravity solutions. Cited in 42 Documents MSC: 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T20 Quantum field theory on curved space or space-time backgrounds 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 16T25 Yang-Baxter equations 83E50 Supergravity 81R12 Groups and algebras in quantum theory and relations with integrable systems 81T60 Supersymmetric field theories in quantum mechanics 14D15 Formal methods and deformations in algebraic geometry Keywords:integrability; AdS/CFT; Yang-Baxter sigma models; supergravity PDFBibTeX XMLCite \textit{B. Hoare} and \textit{S. J. van Tongeren}, J. Phys. A, Math. Theor. 49, No. 43, Article ID 434006, 22 p. (2016; Zbl 1352.81050) Full Text: DOI arXiv