Folding in the Skyrme Model

Conor J. Houghton, Steffen Krusch

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
207 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)4079-4100
Number of pages22
JournalJournal of Mathematical Physics
Volume42
Issue number9
Early online date1 Aug 2001
DOIs
Publication statusPublished - Sep 2001

Bibliographical note

25 pages, 5 figures

Keywords

  • hep-th

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