  Effects of fermionic zero modes (bound states in a vortex core) on the
rotational dynamics of vortices with sponaneously broken axisymmetry are
considered. The results are compared with the Helsinki experiments where the
vortex cores were driven to a fast rotation and torsional oscillations by an
NMR r.f. field (Kondo et al, Phys. Rev. Lett. 67, 81 (1991)). We predict a
resonance NMR absorption on localized states at the external frequency
comparable with the interelevel distance, which is similar to the cyclotron
Landau damping. The resonances can experimentally resolve the localized levels
in vortex cores. For a pure rotation of the core, the effect depends on the
relative signs of the vortex winding number and of the core rotation; thus it
is sensitive to the direction of rotation of the container. The similarity with
the fermionic zero modes on the fundamental strings, which simulate the
thermodynamics of black holes, is discussed.
