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Non-split and split deformations of \({\mathrm{AdS}}_{5}\). (English) Zbl 1354.81047

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.

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
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