### References & Citations

# High Energy Physics - Theory

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

(Submitted on 2 Mar 2021 (v1), last revised 3 May 2021 (this version, v2))

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.

## Submission history

From: Adel Rezaei-Aghdam [view email]**[v1]**Tue, 2 Mar 2021 11:17:19 GMT (21kb)

**[v2]**Mon, 3 May 2021 09:02:19 GMT (22kb)

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