Abstract
The low-energy dynamics of a zero temperature superfluid or of the compressional modes of an ordinary fluid can be described by a simple effective theory for a scalar field — the superfluid ‘phase’. However, when vortex lines are present, to describe all interactions in a local fashion one has to switch to a magnetic-type dual two-form description, which comes with six degrees of freedom (in place of one) and an associated gauge redundancy, and is thus considerably more complicated. Here we show that, in the case of vortex rings and for bulk modes that are much longer than the typical ring size, one can perform a systematic multipole expansion of the effective action and recast it into the simpler scalar field language. In a sense, in the presence of vortex rings the non-single valuedness of the scalar can be hidden inside the rings, and thus out of the reach of the multipole expansion. As an application of our techniques, we compute by standard effective field theory methods the sound emitted by an oscillating vortex ring.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
C.F. Barenghi and R.J. Donnelly, Vortex rings in classical and quantum systems, Fluid Dyn. Res. 41 (2009) 051401.
I.S. Sullivan et al., Dynamics of thin vortex rings, J. Fluid Mech. 609 (2008) 319.
S. Endlich and A. Nicolis, The incompressible fluid revisited: vortex-sound interactions, arXiv:1303.3289 [INSPIRE].
S.S. Gubser, R. Nayar and S. Parikh, Strings, vortex rings and modes of instability, Nucl. Phys. B 892 (2015) 156 [arXiv:1408.2246] [INSPIRE].
B. Horn, A. Nicolis and R. Penco, Effective string theory for vortex lines in fluids and superfluids, JHEP 10 (2015) 153 [arXiv:1507.05635] [INSPIRE].
S.S. Gubser, B. Horn and S. Parikh, Perturbations of vortex ring pairs, Phys. Rev. D 93 (2016) 046001 [arXiv:1510.08059] [INSPIRE].
A. Esposito, R. Krichevsky and A. Nicolis, Vortex precession in trapped superfluids from effective field theory, Phys. Rev. A 96 (2017) 033615 [arXiv:1704.08267] [INSPIRE].
F. Lund and T. Regge, Unified approach to strings and vortices with soliton solutions, Phys. Rev. D 14 (1976) 1524 [INSPIRE].
P. Orland, Extrinsic curvature dependence of Nielsen-Olesen strings, Nucl. Phys. B 428 (1994) 221 [hep-th/9404140] [INSPIRE].
A. Schmitt, Introduction to superfluidity, Lect. Notes Phys. 888 (2015) pp.1-155 [arXiv:1404.1284] [INSPIRE].
A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids, arXiv:1108.2513 [INSPIRE].
A. Nicolis and F. Piazza, Spontaneous symmetry probing, JHEP 06 (2012) 025 [arXiv:1112.5174] [INSPIRE].
D.T. Son, Low-energy quantum effective action for relativistic superfluids, hep-ph/0204199 [INSPIRE].
S. Endlich, A. Nicolis, R. Rattazzi and J. Wang, The quantum mechanics of perfect fluids, JHEP 04 (2011) 102 [arXiv:1011.6396] [INSPIRE].
E. Cremmer and J. Scherk, Spontaneous dynamical breaking of gauge symmetry in dual models, Nucl. Phys. B 72 (1974) 117 [INSPIRE].
W.D. Goldberger, Les Houches lectures on effective field theories and gravitational radiation, hep-ph/0701129 [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
A. Nicolis and R. Penco, Mutual interactions of phonons, rotons and gravity, arXiv:1705.08914 [INSPIRE].
K.W. Schwarz, Three-dimensional vortex dynamics in superfluid He-4: Line-line and line-boundary interactions, Phys. Rev. B 31 (1985) 5782 [INSPIRE].
K.W. Schwarz, Three-dimensional vortex dynamics in superfluid He-4: Homogeneous superfluid turbulence, Phys. Rev. B 38 (1988) 2398 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1709.01927
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Garcia-Saenz, S., Mitsou, E. & Nicolis, A. A multipole-expanded effective field theory for vortex ring-sound interactions. J. High Energ. Phys. 2018, 22 (2018). https://doi.org/10.1007/JHEP02(2018)022
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)022