### 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 language | English |
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Article number | 021B01 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2014 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings : Finite volume size effects.** / Kobayashi, Michikazu; Nitta, Muneto.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Kelvin modes as Nambu-Goldstone modes along superfluid vortices and relativistic strings

T2 - Finite volume size effects

AU - Kobayashi, Michikazu

AU - Nitta, Muneto

PY - 2014

Y1 - 2014

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.

UR - http://www.scopus.com/inward/record.url?scp=84898432841&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898432841&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptu017

DO - 10.1093/ptep/ptu017

M3 - Article

AN - SCOPUS:84898432841

VL - 2014

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 2

M1 - 021B01

ER -