Integrable deformed $$H_{{4}}$$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations

Abstract We show that the Yang–Baxter (YB) deformed backgrounds of the Wess–Zumino–Witten (WZW) model based on the $$H_{{4}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> Lie group can be considered as solutions of the generalized supergravity equations (GSEs). Then, by applying the Poisson–Lie T-duality in the presence of spectator fields, we obtain the non-Abelian target space duals of those models. It is shown that all dual models (except for one model) are integrable and most interestingly, they satisfy the GSEs. As a final remark, we show that all solutions of the GSEs for the original models are trivial.