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Abstract
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Motivated by super Poisson-Lie (PL) symmetry of the Wess-Zumino-Witten (WZW) model based on the $(C^3+A)$ Lie supergroup of our previous
work [A. Eghbali {\it et al.} JHEP 07 (2013) 134], we first obtain and classify all Drinfeld superdoubles (DSDs) generated by the
Lie superbialgebra structures on the $({\C}^3+ {\A})$ Lie superalgebra as a theorem.
Then, introducing a general formulation we find the conditions under which a two-dimensional $\sigma$-model
may be equivalent to a WZW model.
With the help of this formulation and starting the super PL symmetric $(C^3+A)$ 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 $(C^3+A)$ WZW model
does remain invariant under the
super PL T-duality transformation, that is, the model is super PL self-dual.
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