Nonrelativistic Nambu-Goldstone modes propagating along a Skyrmion line

Michikazu Kobayashi, Muneto Nitta

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17 Citations (Scopus)


We study Nambu-Goldstone (NG) modes or gapless modes propagating along a Skyrmion (lump) line in a relativistic and nonrelativistic O(3) sigma model, the latter of which describes isotropic Heisenberg ferromagnets. We show for the nonrelativistic case that there appear two coupled gapless modes with a quadratic dispersion. In addition to the well-known Kelvin mode consisting of two translational zero modes transverse to the Skyrmion line, we show that the other consists of a magnon and dilaton, that is, a NG mode for a spontaneously broken internal U(1) symmetry and a quasi-NG mode for a spontaneously broken scale symmetry of the equation of motion. We find that the commutation relations of Noether charges admit a central extension between the dilatation and phase rotation, in addition to the one between two translations found recently. The counting rule is consistent with the Nielsen-Chadha and Watanabe-Brauner relations only when we take into account quasi-NG modes.

Original languageEnglish
Article number025010
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number2
Publication statusPublished - 2014 Jul 8

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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