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Abstract Motivated by super Poisson–Lie (PL) symmetry of the Wess–Zumino–Witten (WZW) model based on the (C³+A) (C 3 + A) 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 ({C}³+ {A}) (C 3 + A) Lie superalgebra as a theorem. Then, introducing a general formulation we find the conditions under which a two-dimensional σ -model may be equivalent to a WZW model. With the help of this formulation and starting the super PL symmetric (C³+A) (C 3 + A) 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) (C 3 + A) WZW model does remain invariant under the super PL T-duality transformation, that is, the model is super PL self-dual.
Eghbali et al. (Sun,) studied this question.