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

TL;DR

This paper explores the possibility of non-Abelian rotational quasigapless excitations localized on mass vortices in superfluid 3He-B, extending the understanding of vortex excitations beyond traditional Kelvin waves.

Contribution

It proposes the existence of non-Abelian rotational quasigapless modes in superfluid 3He-B vortices, highlighting their potential role alongside known Kelvin waves.

Findings

Non-Abelian rotational quasigapless excitations are argued to exist in 3He-B vortices.

U(1) rotational excitations are well established in asymmetric core vortices.

Coupling between non-Abelian rotational modes and translational modes is discussed.

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.