Yang-Baxter deformations of Minkowski spacetime

Abstract

We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter sigma model description was originally developed for principal chiral models based on a modified classical Yang-Baxter equation. It has been extended to coset curved spaces and models based on the usual classical Yang-Baxter equation. On the other hand, for flat space, there is the obvious problem that the standard bilinear form degenerates if we employ the familiar coset Poincaré group/Lorentz group. Instead we consider a slice of AdS${}_5$ by embedding the 4D Poincaré group into the 4D conformal group $SO(2,4)$. With this procedure we obtain metrics and $B$-fields as Yang-Baxter deformations which correspond to well-known configurations such as T-duals of Melvin backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the T-dual of Grant space, pp-waves, and T-duals of dS${}_4$ and AdS${}_4$. Finally we consider a deformation with a classical $r$-matrix of Drinfeld-Jimbo type and explicitly derive the associated metric and $B$-field which we conjecture to correspond to a new integrable system.

27 pages, no figure, LaTeX

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• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Poisson-Lie T-duals of the bi-Yang-Baxter models
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