Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality

Abstract

By calculating inequivalent classical r-matrices for the $gl(2,\mathbb{R})$ Lie algebra as solutions of (modified) classical Yang-Baxter equation ((m)CYBE)), we classify the YB deformations of Wess-Zumino-Witten (WZW) model on the $GL(2,\mathbb{R})$ Lie group in twelve inequivalent families. Most importantly, it is shown that each of these models can be obtained from a Poisson-Lie T-dual $\sigma$-model in the presence of the spectator fields when the dual Lie group is considered to be Abelian, i.e. all deformed models have Poisson-Lie symmetry just as undeformed WZW model on the $GL(2,\mathbb{R})$. In this way, all deformed models are specified via spectator-dependent background matrices. For one case, the dual background is clearly found.

19 pages, 2 tables, footnote 6 and two references added

References in corpus (8)

• 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
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformation of WZW model based on Lie supergroups: The cases of $GL(1|1)$ and $(C^3+A)$

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• Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model
• Integrable sigma models with Haantjes structure on $H_4$ Lie group