Schrödinger geometries arising from Yang-Baxter deformations

Abstract

We present further examples of the correspondence between solutions of type IIB supergravity and classical $r$-matrices satisfying the classical Yang-Baxter equation (CYBE). In the previous works, classical $r$-matrices have been composed of generators of only one of either $\mathfrak{so}(2,4)$ or $\mathfrak{so}(6)$. In this paper, we consider some examples of $r$-matrices with both of them. The $r$-matrices of this kind contain (generalized) Schrödinger spacetimes and gravity duals of dipole theories. It is known that the generalized Schrödinger spacetimes can also be obtained via a certain class of TsT transformations called null Melvin twists. The metric and NS-NS two-form are reproduced by following the Yang-Baxter sigma-model description.

25 pages, LaTeX, no figure, v2: references and minor clarifications added

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• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• $I$ in generalized supergravity
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Marginal and non-commutative deformations via non-abelian T-duality
• Unimodular jordanian deformations of integrable superstrings
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$