Classical Yang-Baxter Equation from Supergravity

Abstract

We promote the open-closed string map, originally formulated by Seiberg \& Witten, to a solution generating prescription in generalized supergravity. The approach hinges on a knowledge of an antisymmetric bivector $\Theta$, built from antisymmetric products of Killing vectors, which is specified by the equations of motion. In the cases we study, the equations of motion reproduce the Classical Yang-Baxter equation (CYBE) and $\Theta$ is the most general $r$-matrix solution. Our work generalizes Yang-Baxter deformations to non-coset spaces and unlocks gravity as a means to classify $r$-matrix solutions to the CYBE.

arXiv comment6 pages, double column; v2 Schwarzschild example improved, thereby demonstrating that Yang-Baxter deformations can be extended to non-coset geometries

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Cited by in corpus (29)

• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Holographic integration of $T\bar{T}$ and $J\bar{T}$ via $O(d,d)$
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Tri-vector deformations in $d=11$ supergravity
• Classical Yang-Baxter equation from beta-supergravity
• Non-abelian tri-vector deformations in d=11 supergravity
• Polyvector deformations in eleven-dimensional supergravity
• Yang-Baxter Deformation as an O(d,d) Transformation
• Marginal deformations of 3d $\mathcal{N}=2$ CFTs from AdS${}_4$ backgrounds in generalised geometry
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Thirty years of Erice on the brane
• Two-loop conformal invariance for Yang-Baxter deformed strings
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Analytical Structure of the Generalized $\lambda -$deformation
• Generalizing eleven-dimensional supergravity
• Generalized 11D supergravity equations from tri-vector deformations
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Boost generator in AdS_3 integrable superstrings for general braiding
• Tri-vector deformations on compact isometries
• Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations
• Extended Drinfel'd algebras and non-Abelian duality
• Tri-vector deformations with external fluxes
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• Non-isometric U-dualities
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Yang-Baxter structure of the extended space