Quantum exact non-abelian vortices in non-relativistic theories

Muneto Nitta*, Shun Uchino, Walter Vinci

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


Abstract: Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) × U(2) symmetry. We first show, at the classical level, the existence of S3 ≃ S1 ⋉ S2 (S1 fibered over S2) NG modes associated to the breaking U(2) → U(1) on vortices, where S1 and S2 correspond to type I and II NG modes, respectively. We then show, by using a Bethe ansatz technique, that the U(1) symmetry is restored, while the SU(2) symmery remains broken non-pertubatively at quantum level. Accordingly, the U(1) NG mode turns into a c = 1 conformal field theory, the Tomonaga-Luttinger liquid, while the S2 NG mode remains gapless, describing a ferromagnetic liquid. This allows the vortex to be genuinely non-Abelian at quantum level.

Original languageEnglish
Article number98
JournalJournal of High Energy Physics
Issue number9
Publication statusPublished - 2014
Externally publishedYes


  • Bethe Ansatz
  • Sigma Models
  • Solitons Monopoles and Instantons
  • Spontaneous Symmetry Breaking

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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