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Target space supergeometry of \(\eta\) and \(\lambda\)-deformed strings. (English) Zbl 1390.81412
Summary: We study the integrable \(\eta\) and \(\lambda\)-deformations of supercoset string sigma models, the basic example being the deformation of the \(\mathrm{AdS}_{5}\times S^{5}\) superstring. We prove that the kappa symmetry variations for these models are of the standard Green-Schwarz form, and we determine the target space supergeometry by computing the superspace torsion. We check that the \(\lambda\)-deformation gives rise to a standard (generically type II*) supergravity background; for the \(\eta\)-model the requirement that the target space is a supergravity solution translates into a simple condition on the \(R\)-matrix which enters the definition of the deformation. We further construct all such non-abelian \(R\)-matrices of rank four which solve the homogeneous classical Yang-Baxter equation for the algebra \( \mathfrak{so} (2, 4)\). We argue that most of the corresponding backgrounds are equivalent to sequences of non-commuting TsT-transformations, and verify this explicitly for some of the examples.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E50 Supergravity
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