All Jordanian deformations of the $AdS_5 \times S^5$ superstring

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Abstract
We explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on \mathfrak{psu}(2,2|4) ???? ???? ???? ( 2 , 2 | 4 ) , corresponding to Jordanian Yang-Baxter deformations of the AdS_5\times S^5 A d S 5 × 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.
Funding Information
  • Agencia Estatal de Investigación (PID2020-114157GB-I00)
  • European Regional Development Fund
  • National Science Foundation (PHY-1748958)
  • Xunta de Galicia (ED431C-2021/14)
  • 'la Caixa' Foundation (LCF/BQ/PI19/11690019)

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