A nonlocal Poisson bracket of the sine-Gordon model

TL;DR

This paper explores the nonlocal Poisson structure of the sine-Gordon model derived from the nonabelian dual of the classical string on a two-sphere, revealing a projection from the dual string phase space to sine-Gordon.

Contribution

It demonstrates a projection map linking the phase space of the nonabelian dual string to the sine-Gordon model and characterizes its nonlocal Poisson structure.

Findings

Established a projection from dual string phase space to sine-Gordon

Identified the sine-Gordon Poisson structure as nonlocal with one integration

Connected classical string duality to nonlocal Poisson brackets

Abstract

It is well known that the classical string on a two-sphere is more or less equivalent to the sine-Gordon model. We consider the nonabelian dual of the classical string on a two-sphere. We show that there is a projection map from the phase space of this model to the phase space of the sine-Gordon model. The corresponding Poisson structure of the sine-Gordon model is nonlocal with one integration.