Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings

Finite volume size effects

Michikazu Kobayashi, Muneto Nitta

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 the infinite volume limit. On the other hand, in a system with finite volume, we find an imaginary massive gap causing 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.

Original languageEnglish
Article number021B01
JournalProgress of Theoretical and Experimental Physics
Volume2014
Issue number2
DOIs
Publication statusPublished - 2014

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strings
vortices
relativistic theory
wavelengths
energy

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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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 the infinite volume limit. On the other hand, in a system with finite volume, we find an imaginary massive gap causing 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.",
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N2 - 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 the infinite volume limit. On the other hand, in a system with finite volume, we find an imaginary massive gap causing 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.

AB - 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 the infinite volume limit. On the other hand, in a system with finite volume, we find an imaginary massive gap causing 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.

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