  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.
