All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring

Abstract

We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $Ad{S}_5\times S^5$ superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number $N<32$ of supercharges that can be $N=12,8,6,4,0$.

arXiv comment39 pages, 2 appendices, many tables, v2: expanded conclusions, missing unimodular R_6 solutions included, updated discussion on so(6) shifts, various minor changes to address the referee reports

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