2025/11/08 by Eghbali, Ali, Hosseinpour-Sadid, Meysam, Rezaei-Aghdam, Adel
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2511.05959
In superdimension (2|2) there are only three non-Abelian Lie superalgebras admitting non-degenerate ad-invariant supersymmetric metric, the well-known Lie superalgebra gl(1|1), and two more, (\C3 + \A) and (\C05 +\A). After a brief review of the construction of the Wess-Zumino-Witten (WZW) models based on the GL(1|1) and (C3 + A) Lie supergroups, we proceed to construct the WZW model on the (C05 +A) Lie supergroup. Unfortunately, this model does not include the super Poisson-Lie symmetry. In the following, three new exact conformal field theories of the WZW type are constructed by gauging an anomaly-free subgroup SO(2) of the Lie supergroups mentioned above. The most interesting indication of this work is that the gauged WZW model on the supercoset (C3 + A)/SO(2) has super Poisson-Lie symmetry; most importantly, its dual model is conformally invariant at the one-loop order, and this is presented here for the first time. Finally, in order to study the Yang-Baxter (YB) deformations of the (C05 +A) WZW model we obtain the inequivalent solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) for the (\C05 +\A) Lie superalgebra. Then, we classify all possible YB deformations for the (C05 +A) and settle also the issue of an one-loop conformality of the deformed backgrounds. The classification results are important, in particular in the Lie supergroup case they are rare, much hard technical work was needed to obtain them.