Poisson-Lie sigma models over low dimensional real Poisson-Lie groups

TL;DR

This paper explores Poisson-Lie sigma models on low-dimensional real Poisson-Lie groups, revealing their topological and BF gauge model structures, thus advancing understanding of their mathematical and physical properties.

Contribution

It identifies specific low-dimensional Poisson-Lie groups where the sigma models are topological or BF gauge models, highlighting new model structures in nonsemisimple cases.

Findings

Models on 2, 3, and some 4-dimensional groups identified

Models over G and its dual are topological or BF gauge models

Advances understanding of Poisson-Lie sigma models in low dimensions

Abstract

The Poisson-Lie sigma models over nonsemisimple low dimensional real Poisson-Lie groups are investigated. We find two sided models on two, three and some four dimensional Poisson-Lie groups where the Poisson-Lie sigma models over Poisson-Lie groups G and its dual $\tilde{G}$ are topological sigma models or BF gauge models.