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. Non-Abelian rotational quasigapless excitations could appear on the mass vortices in the B phase of the superfluid ${}^3\mathrm{He}$, due to the fact that the order parameter in ${}^3\mathrm{He}$-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.

• Received 25 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.081702