Yang-Baxter deformations of WZW model on the Heisenberg Lie group

Abstract

The Yang-Baxter (YB) deformations of Wess-Zumino-Witten (WZW) model on the Heisenberg Lie group ($H_4$) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the $h_4$ Lie algebra by using its corresponding automorphism transformation. Then we show that YB deformations of $H_4$ WZW model are split into ten nonequivalent backgrounds including metric and $B$-field such that some of the metrics of these backgrounds can be transformed to the metric of $H_4$ WZW model while the antisymmetric $B$-fields are changed. The rest of the deformed metrics have a different isometric group structure than the $H_4$ WZW model metric. As an interesting result, it is shown that all new integrable backgrounds of the YB deformed $H_4$ WZW model are conformally invariant up to two-loop order. In this way, we obtain the general form of the dilaton fields satisfying the vanishing beta-function equations of the corresponding $\sigma$-models.

24 pages, some references are added

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• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Abelian Yang-Baxter Deformations and TsT transformations
• Yang-Baxter sigma models based on the CYBE
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
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• Generalized Supergravity Equations for the WZW Model
• Integrable sigma models with complex and generalized complex structures
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
• Yang-Baxter deformations of the OSP(1|2) WZW model
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Integrable sigma models with Haantjes structure on $H_4$ Lie group