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 (H4) are examined. We proceed to obtain the nonequivalent solutions of (modified) classical Yang-Baxter equation ((m)CYBE) for the h4 Lie algebra by using its corresponding automorphism transformation. Then we show that YB deformations of H4 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 H4 WZW model while the antisymmetric B-fields are changed. The rest of the deformed metrics have a different isometric group structure than the H4 WZW model metric. As an interesting result, it is shown that all new integrable backgrounds of the YB deformed H4 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 σ-models.