Skyrmions, instantons, mass and curvature

TL;DR

The paper demonstrates that massless Skyrmions in hyperbolic space can approximate massive Skyrmions in Euclidean space, and introduces a method to approximate massive Skyrmions via instanton holonomy, extending previous massless approximations.

Contribution

It generalizes the instanton holonomy approximation from massless to massive pions, linking hyperbolic and Euclidean Skyrmions through curvature and mass relationships.

Findings

Massless hyperbolic Skyrmions approximate massive Euclidean Skyrmions effectively.

Holonomy along circles of instantons can model massive pion Skyrmions.

Provides a new geometric approach to Skyrmion approximation methods.

Abstract

We show that Skyrmions with massless pions in hyperbolic space provide a good approximation to Skyrmions with massive pions in Euclidean space, for a particular relationship between the pion mass and the curvature of hyperbolic space. Using this result we describe how a Skyrmion with massive pions in Euclidean space can be approximated by the holonomy along circles of a Yang-Mills instanton. This is a generalization of the approximation of Skyrmions by the holonomy along lines of an instanton, which is only applicable to massless pions.