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

Abstract

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 $({\mathcal{C}}^3+\mathcal{A})$ 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.

arXiv comment27 pages, 1 table, 1 figure, 1 appendix, v3 minor changes

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• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Generalized Supergravity Equations for the WZW Model
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations