A hierarchy of WZW models related to super Poisson-Lie T-duality

Motivated by super Poisson-Lie (PL) symmetry of the Wess-Zumino-Witten (WZW) model based on the (C3+A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(C<^>3+A)$$\end{document} Lie supergroup of our previous work (Eghbali et al., in J High Energy Phys 07:134, 2013. arXiv:1303.4069 [hep-th]), we first obtain and classify all Drinfeld superdoubles (DSDs) generated by the Lie superbialgebra structures on the (C3+A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathscr {C}}<^>3+ {\mathscr {A}})$$\end{document} Lie superalgebra as a theorem. Then, introducing a general formulation we find the conditions under which a two-dimensional sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-model may be equivalent to a WZW model. With the help of this formulation and starting the super PL symmetric (C3+A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(C<^>3+A)$$\end{document} WZW model, we get a hierarchy of WZW models related to super PL T-duality, in such a way that it is different from the super PL T-plurality, because the DSDs are, in this process, non-isomorphic. The most interesting indication of this work is that the (C3+A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(C<^>3+A)$$\end{document} WZW model does remain invariant under the super PL T-duality transformation, that is, the model is super PL self-dual.