Hopf Soliton Solutions from Low Energy Effective Action of SU(2) 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 another fourth-order term which destabilizes the soliton solution. In this paper we derive an extended action including second derivative terms and obtain soliton solutions numerically. A new topological lower bound formula is infered for the extended action.

arXiv comment18 pages, 7 figures

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Cited by in corpus (4)

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• Static Hopfions in the extended Skyrme-Faddeev model
• Some vortex solutions in the extended Skyrme-Faddeev model