Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles

TL;DR

This paper presents a unified Hamiltonian framework for constructing integrable deformations of sigma models, revealing their Poisson-Lie T-duality and encompassing Yang-Baxter and gauged WZW types.

Contribution

It introduces a systematic Hamiltonian approach that unifies different integrable deformation methods and demonstrates their duality.

Findings

Unified framework for integrable sigma-model deformations

Demonstration of Poisson-Lie T-duality between deformation types

Applicability to Yang-Baxter and gauged WZW deformations

Abstract

We describe a unifying framework for the systematic construction of integrable deformations of integrable $\sigma$-models within the Hamiltonian formalism. It applies equally to both the `Yang-Baxter' type as well as `gauged WZW' type deformations which were considered recently in the literature. As a byproduct, these two families of integrable deformations are shown to be Poisson-Lie T-dual of one another.