The Skyrme model and chiral perturbation theory

TL;DR

This paper derives a Lagrangian for soliton-background interactions in sigma models, showing that the Skyrme model's quantization aligns with the leading terms of chiral perturbation theory, suggesting a low-energy connection.

Contribution

It introduces a Lagrangian for soliton interactions with background fields in sigma models and demonstrates its agreement with chiral perturbation theory in the Skyrme model context.

Findings

The derived Lagrangian modifies soliton dynamics via potential and metric effects.

Quantization of the Lagrangian matches the leading pion-nucleon terms.

Chiral perturbation theory can be viewed as a low-energy limit of the Skyrme model.

Abstract

A lagrangian which describes interactions between a soliton and a background field is derived for sigma models whose target is a symmetric space. The background field modifies the usual moduli space approximation to soliton dynamics in two ways: by introducing a potential energy, and by inducing a Kaluza-Klein metric on the moduli space. In the particular case of the Skyrme model, this lagrangian is quantised and shown to agree with the leading pion-nucleon term in the chiral effective lagrangian, which is widely used in theoretical nuclear physics. Thus chiral perturbation theory could be considered a low energy limit of the Skyrme model.