Extended Soliton Solutions in an Effective Action for SU(2) Yang-Mills Theory

TL;DR

This paper demonstrates that by perturbatively including a second derivative term, stable soliton solutions can be obtained in an extended effective action for SU(2) Yang-Mills theory, addressing previous stability issues.

Contribution

It introduces a perturbative approach to incorporate second derivative terms, enabling stable soliton solutions in an extended SFN model derived from Yang-Mills theory.

Findings

Stable soliton solutions are achieved with the second derivative term.

The perturbative method reduces instability caused by higher-order terms.

The extended model aligns with the infrared behavior of Yang-Mills theory.

Abstract

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce) the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.