Hamiltonian Approach to Poisson Lie T-Duality

TL;DR

This paper explores the Hamiltonian formalism as a natural framework for Poisson Lie T-duality, demonstrating its invariance and applying it to specific models like the O(3) nonlinear sigma-model.

Contribution

It introduces a Hamiltonian approach to Poisson Lie T-duality, providing dual formulations and recovering known dual systems from a general quadratic Hamiltonian.

Findings

Dual Hamiltonian formulation of the O(3) nonlinear sigma-model

Recovery of known Poisson Lie T-dual systems from a quadratic Hamiltonian

Poisson structures underpin T-duality independent of Hamiltonian choice

Abstract

The Hamiltonian formalism offers a natural framework for discussing the notion of Poisson Lie T-duality. This is because the duality is inherent in the Poisson structures alone and exists regardless of the choice of Hamiltonian. Thus one can pose alternative dynamical systems possessing nonabelian T-duality. As an example, we find a dual Hamiltonian formulation of the O(3) nonlinear sigma-model. In addition, starting from a general quadratic Hamiltonian, we easily recover the known dynamical systems having Poisson Lie T-duality.