Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings: finite volume size effects

Understand

We study Kelvin modes and translational zero modes excited along a quantized vortex and relativistic global string in superfluids and a relativistic field theory, respectively, by constructing the low-energy effective theory of these modes.

• We find that they become exact gapless Nambu-Goldstone modes only in a system with infinite volume limit.
• On the other hand, in a system with the finite volume, we find an imaginary massive gap causing the tachyonic instability above some critical wavelength in the relativistic theory.
• We also find in the non-relativistic theory that Kelvin modes with wavelengths longer than some critical value propagate in the direction opposite to those with shorter length, contrary to conventional understanding.