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

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.

9 pages, v2: published version

References in corpus (3)

• Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• Kelvin Waves of Quantized Vortex Lines in Trapped Bose-Einstein Condensates

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• Noncommuting Momenta of Topological Solitons
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Non-relativistic Nambu-Goldstone modes propagating along a skyrmion line
• Collective excitations of a quantized vortex in ${}^3{P}_2$ superfluids in neutron stars
• Interpolating relativistic and non-relativistic Nambu-Goldstone and Higgs modes
• Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice
• Kelvin wave in miscible two-component Bose-Einstein condensates
• Kelvin-Wave-Inspired Optical Vortex Excitation in Kerr Nonlinear Media