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Abstract
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In superdimension (2|2) there are only three non-Abelian Lie superalgebras gl(1|1), (C^3+A) and (C^5_0+A) admitting ad-invariant supersymmetric and non-degenerate bilinear form. We present here Wess-Zumino-Witten (WZW) models based on the Lie supergroups GL(1|1), (C^3+A). Then, we proceed to construct the WZW model over the (C^5_0+A) Lie supergroup. We examine in details the (C^3+A) case and, by gauging an appropriate Abelian subgroup, string background of superdimension (1|2) is obtained.
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