Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model

Abstract

We propose that the Yang-Baxter deformation of the symmetric space sigma-model parameterized by an r-matrix solving the homogeneous (classical) Yang-Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS_5 sigma-model. The same should also be true for the full AdS_5 x S^5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang-Baxter deformations based on non-abelian r-matrices to the undeformed AdS_5 x S^5 model by a combination of T-dualities and non-linear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.

28 pages; v2: comments and references added; v3: 29 pages, typos corrected and reference added

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• $T$-folds from Yang-Baxter deformations
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• $I$ in generalized supergravity
• Generalized Dualities and Higher Derivatives
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Unimodular jordanian deformations of integrable superstrings
• Non-abelian U-duality at work
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Topological Gauging and Double Current Deformations
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• Generalized Supergravity Equations and Generalized Fradkin-Tseytlin Counterterm
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• Super Non-Abelian T-Duality
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Integrability of the $\lambda$-deformation of the PCM with spectators
• Yang-Baxter deformations of the flat space string
• Investigating (Non)-Integrability and Pulsating String in D3-Brane Background
• Generalized Supergravity Equations for the WZW Model
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations