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arXiv · 2103.01646

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

Ali Eghbali·Tayebe Parvizi·Adel Rezaei-Aghdam
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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.

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Ali Eghbali, Tayebe Parvizi, Adel Rezaei-Aghdam. 2021-03-02. Yang-Baxter deformations of WZW model on the Heisenberg Lie group. https://doi.org/10.1016/j.nuclphysb.2021.115423

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