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

TL;DR

This paper classifies all Jordanian Yang-Baxter deformations of the $AdS_5 imes S^5$ superstring, preserving integrability and identifying their supergravity solutions and supersymmetry properties.

Contribution

It explicitly constructs and classifies all Jordanian solutions of the classical Yang-Baxter equation on $rak{psu}(2,2|4)$, expanding understanding of integrable deformations of the superstring.

Findings

Deformations preserve classical integrability of the sigma-model.

Unimodular solutions lead to supergravity solutions with reduced supersymmetry.

Classified solutions include backgrounds with 0, 4, 6, 8, or 12 supercharges.

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 $AdS_5\times S^5$ 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 $N=12,8,6,4,0$.