Euclidean 4d exact solitons in a Skyrme type model

TL;DR

This paper introduces a four-dimensional Euclidean Skyrme-like model with exact soliton solutions, which could provide insights into the low-energy behavior of SU(2) Yang-Mills theory.

Contribution

It presents a novel 4d Euclidean field theory with exact soliton solutions, reducing complex equations to linear ODEs via a special ansatz.

Findings

Constructed infinite exact soliton solutions with zero Euclidean action

Identified a mass scale influencing soliton size beyond Derrick's scaling

Potential relevance to low-energy SU(2) Yang-Mills theory

Abstract

We introduce a Skyrme type, four dimensional Euclidean field theory made of a triplet of scalar fields n, taking values on the sphere S^2, and an additional real scalar field phi, which is dynamical only on a three dimensional surface embedded in R^4. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory.