Local $\beta$-deformations and Yang-Baxter sigma model

Abstract

Homogeneous Yang-Baxter (YB) deformation of AdS${}_5\times$S${}^5$ superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to $\beta$-deformations of the AdS${}_5\times$S${}^5$ background when the classical $r$-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10,10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing $H$-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study $\beta$-deformations of $H$-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.

95 pages; v2: clarifications and references added; v3: published version

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• Generalized Dualities and Higher Derivatives
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Tri-vector deformations in $d=11$ supergravity
• Dressing cosets and multi-parametric integrable deformations
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• Non-abelian U-duality at work
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• SUSY and the bi-vector
• Type II Double Field Theory in Superspace
• Jacobi-Lie Models and Supergravity Equations
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• Non-isometric U-dualities
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations