Hoare, Ben; van Tongeren, Stijn J. Non-split and split deformations of \({\mathrm{AdS}}_{5}\). (English) Zbl 1354.81047 J. Phys. A, Math. Theor. 49, No. 48, Article ID 484003, 35 p. (2016). Summary: The \(\eta\) deformation of the \({\mathrm{AdS}}_{5}\times {S}^{5}\) superstring depends on a non-split \(r\) matrix for the superalgebra \({\mathfrak{psu}}(2,2| 4)\). Much of the investigation into this model has considered one particular choice, however there are a number of inequivalent alternatives. This is also true for the bosonic sector of the theory with \({\mathfrak{su}}(2,2)\), the isometry algebra of \({\mathrm{AdS}}_{5}\), admitting one split and three non-split \(r\) matrices. In this article we explore these \(r\) matrices and the corresponding geometries. We investigate their contraction limits, comment on supergravity backgrounds and demonstrate their relation to gauged-WZW deformations. We then extend the three non-split cases to \({\mathrm{AdS}}_{5}\times {S}^{5}\) and compute four separate bosonic two-particle tree-level \(S\)-matrices based on inequivalent BMN-type light-cone gauges. The resulting \(S\)-matrices, while different, are related by momentum-dependent one-particle changes of basis. Cited in 20 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 81T10 Model quantum field theories 81R12 Groups and algebras in quantum theory and relations with integrable systems 81U20 \(S\)-matrix theory, etc. in quantum theory 14D15 Formal methods and deformations in algebraic geometry 81T60 Supersymmetric field theories in quantum mechanics 17A70 Superalgebras 83E50 Supergravity Keywords:deformations of \({\mathrm{AdS}}_{5} \times S^5\); integrable string sigma models; \(q\)-deformed symmetries; \(S\)-matrix PDFBibTeX XMLCite \textit{B. Hoare} and \textit{S. J. van Tongeren}, J. Phys. A, Math. Theor. 49, No. 48, Article ID 484003, 35 p. (2016; Zbl 1354.81047) Full Text: DOI arXiv