Poisson-Lie T-plurality for WZW backgrounds

Poisson-Lie T-plurality constructs a chain of supergravity solutions from a Poisson-Lie symmetric solution. We study the Poisson-Lie T-plurality for supergravity solutions with $H$-flux, which are not Poisson-Lie symmetric but admit non-Abelian isometries, $\mathcal{L}_{v_a}g_{mn}=0$ and $\mathcal{L}_{v_a}H_3=0$ with $\mathcal{L}_{v_a}B_2\neq 0$. After introducing the general procedure, we study the Poisson-Lie T-plurality for two WZW backgrounds, the AdS$_3$ with $H$-flux and the Nappi-Witten background.