New classical r-matrices from integrable non-linear sigma models

TL;DR

This paper investigates the integrable structure of non-linear sigma models on symmetric spaces, revealing a field-dependent r-matrix satisfying a dynamical Yang-Baxter equation that governs their Poisson brackets.

Contribution

It introduces a novel field-dependent r-matrix framework for the canonical structure of integrable sigma models on symmetric spaces, connecting to dynamical Yang-Baxter equations.

Findings

Fundamental Poisson brackets are governed by a non antisymmetric, field-dependent r-matrix.

The r-matrix satisfies a dynamical Yang-Baxter equation.

The analysis advances understanding of the algebraic structure underlying integrable sigma models.

Abstract

Non linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non-linear sigma models which are known to be integrable. Using the current algebra structure of these models their canonical structure is analysed and it is shown that their non ultralocal fundamental Poisson bracket relation is governed by a field dependent non antisymmetric r-matrix obeying a dynamical Yang Baxter equation. Contribution presented at the XIX ICGTMP Salamanca June 92