Eur. Phys. J. C (2023) 83: 917
https://doi.org/10.1140/epjc/s10052-023-12084-8

Regular Article - Theoretical Physics

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

Department of Physics, Faculty of Basic Sciences, Azarbaijan Shahid Madani University, 53714-161, Tabriz, Iran

^c rezaei-a@azaruniv.ac.ir

Received: 23 May 2023
Accepted: 27 September 2023
Published online: 11 October 2023

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.