Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model

Abstract

We construct an integrable sigma model with a generalized $\mathcal{F}$ structure, which involves a generalized Nijenhuis structure $\mathcal{J}$ satisfying ${\mathcal{J}}^3=-\mathcal{J}$. Utilizing the expression of the generalized complex structure on the metric Lie group manifold $G$ in terms of operator relations on its Lie algebra $\mathfrak{g}$, we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.

14 pages, two refs are added

References in corpus (3)

• Yang-Baxter sigma models based on the CYBE
• Yang-Baxter deformations of WZW model on the Heisenberg Lie group
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality

Cited by in corpus (1)

• Integrable sigma models with Haantjes structure on $H_4$ Lie group