More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations

Abstract

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, $({\C}^3 + \A)$ and $({\C}_0^5 +{\A})$. After a brief review of the construction of the Wess-Zumino-Witten (WZW) models based on the $GL(1|1)$ and $(C^3+A)$ Lie supergroups, we proceed to construct the WZW model on the $(C_0^5+A)$ 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 $(C^3+A)/$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 $(C_0^5+A)$ WZW model we obtain the inequivalent solutions of the (modified) graded classical Yang-Baxter equation ((m)GCYBE) for the $({\C}_0^5 +{\A})$ Lie superalgebra. Then, we classify all possible YB deformations for the $(C_0^5+A)$ 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.

39 pages, to appear in Fortschr. Phys

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Cited by in corpus (1)

• Integrable sigma models with Haantjes structure on $H_4$ Lie group