Icosahedral Skyrmions

Richard Battye, Conor Houghton, Paul Sutcliffe

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

13 Citations (Scopus)
218 Downloads (Pure)


In this paper we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize the energy of Coulomb charges on a sphere, we are led to conjecture a sequence of magic baryon numbers, B=7,17,37,67,97,... at which the minimal energy Skyrmion has icosahedral symmetry and unusually low energy. We present evidence for this conjecture by applying a simulated annealing algorithm to compute energy minimizing rational maps for all degrees upto 40. Further evidence is provided by the explicit construction of icosahedrally symmetric rational maps of degrees 37, 47, 67 and 97. To calculate these maps we introduce two new methods for computing rational maps with Platonic symmetries.
Original languageEnglish
Pages (from-to)3543-3554
Number of pages12
JournalJournal of Mathematical Physics
Issue number8
Publication statusPublished - Aug 2003

Bibliographical note

15 pages, including 4 figures


  • hep-th


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