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

TL;DR

This paper investigates how finite volume effects influence Kelvin modes and Nambu-Goldstone modes along superfluid vortices and relativistic strings, revealing instabilities and unconventional propagation behaviors.

Contribution

It provides a low-energy effective theory showing finite volume induces gaps and instabilities in Kelvin and Nambu-Goldstone modes, extending understanding of these excitations.

Findings

Exact gapless modes only in infinite volume

Finite volume causes tachyonic instability above a critical wavelength

Kelvin modes can propagate opposite to conventional expectations

Abstract

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. The number of Nambu-Goldstone modes also saturate the equality of the Nielsen-Chadha inequality for both relativistic and non-relativistic theories.