Folding in the Skyrme Model

Abstract

There are only three stable singularities of a differentiable map between three-dimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU(2), and its singularities correspond to the points where the baryon density vanishes. In this paper we consider the singularity structure of Skyrme configurations. The Skyrme model can only be solved numerically. However, there are good analytic ansaetze. The simplest of these, the rational map ansatz, has a non-generic singularity structure. This leads us to introduce a non-holomorphic ansatz as a generalization. For baryon number two, three and four, the approximate solutions derived from this ansatz are closer in energy to the true solutions than any other ansatz solution. We find that there is a tiny amount of negative baryon density for baryon number three, but none for two or four. We comment briefly on the relationship to Bogomolny-Prasad-Sommerfield monopoles.

25 pages, 5 figures

References in corpus (2)

• Solitonic fullerene structures in light atomic nuclei
• Skyrmions on the Two-Sphere

Cited by in corpus (8)

• Homotopy of Rational Maps and the Quantization of Skyrmions
• Finkelstein-Rubinstein constraints for the Skyrme model with pion masses
• New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
• The BPS sectors of the Skyrme model and their non-BPS extensions
• Negative Baryon density and the Folding structure of the B=3 Skyrmion
• An Improved Harmonic Map Ansatz
• False vacuum Skyrmions revisited
• Locations of JNR skyrmions