Non-Abelian Quasi-Gapless Modes Localized on Mass Vortices in Superfluid 3He-B

Abstract

Kelvin waves or Kelvons have been known for a long time as gapless excitations propagating along superfluid vortices. These modes can be interpreted as the Nambu-Goldstone excitations arising from the spontaneous breaking of the translational symmetry. Recently a different type of gapless excitation localized on strings -- the so-called non-Abelian mode -- attracted much attention in high-energy physics. We discuss their relevance in condensed matter physics. Although we failed to find exactly gapless non-Abelian modes, non-Abelian rotational quasigapless excitations are argued to exist on the mass vortices in the B phase of the superfluid 3He, due to the fact that the order parameter in 3He-B is tensorial. While the U(1) rotational excitations are well established in vortices with asymmetric cores, the non-Abelian rotational excitations belonging to the same family were not considered. In the general case they are coupled with the translational modes.

arXiv comment12 pages, 1 figure; v2: published version with minor corrections

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• Calculating Extra (Quasi)Moduli on the Abrikosov-Nielsen-Olesen string with Spin-Orbit Interaction
• Q-lumps on a Domain Wall with a Spin-Orbit Interaction
• Non-Abelian Moduli on Domain Walls
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• Low energy dynamics of gapless and quasi-gapless modes of vortices in superfluid ${}^3$He-B
• Deformation of the CP(1) model leading to fixed size solitons in 2+1 dimensions