Classification of Poisson-Lie T-dual models with two-dimensional targets

TL;DR

This paper classifies four-dimensional Manin triples and Drinfeld doubles, constructing corresponding two-dimensional Poisson-Lie T-dual sigma models, and presents an example with a unique decomposition into different Manin triples.

Contribution

It provides a comprehensive classification of four-dimensional Manin triples and Drinfeld doubles, and constructs associated Poisson-Lie T-dual sigma models, including a novel example with nontrivial decomposition.

Findings

Classification of four-dimensional Manin triples and Drinfeld doubles

Construction of Poisson-Lie T-dual sigma models on these structures

An example of a Drinfeld double with two different Manin triple decompositions

Abstract

Four-dimensional Manin triples and Drinfeld doubles are classified and corresponding two-dimensional Poisson-Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two nontrivially different Manin triples is presented.