Dual Instantons

TL;DR

This paper demonstrates a duality mapping of Belavin-Polyakov instantons in the O(3) nonlinear sigma model to nontopological solitons in a dual theory, revealing their stationary nature and on-shell action equivalence.

Contribution

It introduces a dual formulation where instantons are represented as nontopological solitons, providing new insights into their properties and relationships.

Findings

Instantons map to nontopological solitons in the dual theory

Dual action and original sigma model action agree on shell

Stationary points correspond to instantons and solitons

Abstract

We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear $\sigma-$model to a dual theory where they then appear as nontopological solitons. They are stationary points of the Euclidean action in the dual theory, and moreover, the dual action and the O(3)-nonlinear $\sigma-$model action agree on shell.