Classical Yang-Baxter equation from beta-supergravity

Abstract

Yang-Baxter deformations of superstring sigma-models have recently inspired a supergravity solution generating technique. Using the open/closed string map and a Killing bi-vector as a deformation parameter, new solutions can be built, such that the (generalised) supergravity field equations were conjectured to always reduce to the classical Yang-Baxter equation (CYBE). In this work we provide a proof of this conjecture, using a systematic approach based on the so-called $\beta$-supergravity, which is a dynamical theory for the field ${\beta }^{mn}$ instead of the NSNS 2-form $b_{mn}$.

arXiv comment19 pages; v2: references updated; v3: published version

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• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Generalized Dualities and Higher Derivatives
• Tri-vector deformations in $d=11$ supergravity
• Dressing cosets and multi-parametric integrable deformations
• Non-abelian tri-vector deformations in d=11 supergravity
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Polyvector deformations in eleven-dimensional supergravity
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• Non-Abelian T-duality as a Transformation in Double Field Theory
• Non-abelian U-duality at work
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• SUSY and the bi-vector
• Integrability structures in string theory
• Extended Drinfel'd algebras and non-Abelian duality
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