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

TL;DR

This paper develops integrable sigma models incorporating generalized complex and Nijenhuis structures, extending Yang-Baxter models and introducing multi-structure variants with explicit examples.

Contribution

It introduces new integrable sigma models with generalized $ ext{F}$ and complex structures, including multi-Yang-Baxter models with multiple compatible Nijenhuis structures.

Findings

Constructed an integrable sigma model with generalized $ ext{F}$ structure.

Formulated Yang-Baxter sigma models with generalized complex structures.

Presented multi-Yang-Baxter models with multiple compatible Nijenhuis structures.

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.