Poisson–Lie T-plurality for WZW backgrounds

Abstract

Abstract 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, $\pounds_{v_a}g_{mn}=0$ and $\pounds_{v_a}H_3=0$ with $\pounds_{v_a}B_2\neq 0$. After introducing the general procedure, we study the Poisson–Lie $T$-plurality for two Wess–Zumino–Witten backgrounds, AdS$_3$ with $H$-flux and the Nappi–Witten background.