Abstract
We consider the superfluid phase of a specific renormalizable relativistic quantum field theory. We prove that, within the regime of validity of perturbation theory and of the superfluid effective theory, there are consistent and regular vortex solutions where the superfluid’s velocity field as traditionally defined smoothly interpolates between zero and arbitrarily large superluminal values. We show that this solution is free of instabilities and of superluminal excitations. We show that, in contrast, a generic vortex solution for an ordinary fluid does develop an instability if the velocity field becomes superluminal. All this questions the characterization of a superfluid velocity field as the actual velocity of “something”.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Annals Phys. 118 (1979) 341 [INSPIRE].
A. Joyce, A. Nicolis, A. Podo and L. Santoni, Integrating out beyond tree level and relativistic superfluids, JHEP 09 (2022) 066 [arXiv:2204.03678] [INSPIRE].
E. Babichev, S. Ramazanov and A. Vikman, Recovering P(X) from a canonical complex field, JCAP 11 (2018) 023 [arXiv:1807.10281] [INSPIRE].
E.J. Weinberg, Classical solutions in quantum field theory: Solitons and Instantons in High Energy Physics, Cambridge University Press (2012) [https://doi.org/10.1017/CBO9781139017787] [INSPIRE].
A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
A. Nicolis and R. Rattazzi, Classical and quantum consistency of the DGP model, JHEP 06 (2004) 059 [hep-th/0404159] [INSPIRE].
I. Kourkoulou, A. Nicolis and K. Parmentier, Low-temperature thermal corrections to a superfluid’s equation of state, arXiv:2212.12555 [INSPIRE].
S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, Microcausality in curved space-time, Phys. Rev. D 77 (2008) 084016 [arXiv:0709.1483] [INSPIRE].
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
A. Nicolis and R. Penco, Mutual Interactions of Phonons, Rotons, and Gravity, Phys. Rev. B 97 (2018) 134516 [arXiv:1705.08914] [INSPIRE].
A. Nicolis, R. Penco, F. Piazza and R. Rattazzi, Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155 [arXiv:1501.03845] [INSPIRE].
A. Nicolis, F. Piazza and K. Zeghari, Rotating cosmologies: classical and quantum, JCAP 10 (2022) 059 [arXiv:2204.04110] [INSPIRE].
B. Carter and D. Langlois, The equation of state for cool relativistic two constituent superfluid dynamics, Phys. Rev. D 51 (1995) 5855 [hep-th/9507058] [INSPIRE].
A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids, arXiv:1108.2513 [INSPIRE].
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, in W.A. Benjamin, Frontiers in Physics: a lecture note and reprint series, Advanced Book Program (1975).
M.J. Landry, Non-equilibrium effective field theory and second sound, JHEP 04 (2021) 213 [arXiv:2008.11725] [INSPIRE].
P.C. Martin, O. Parodi and P.S. Pershan, Unified hydrodynamic theory for crystals, liquid crystals, and normal fluids, Phys. Rev. A 6 (1972) 2401.
L.P. Pitaevskii, Second sound in solids, Sov. Phys. Usp. 11 (1968) 342.
G. Cuomo and Z. Komargodski, Giant Vortices and the Regge Limit, JHEP 01 (2023) 006 [arXiv:2210.15694] [INSPIRE].
Acknowledgments
We would like to thank Matteo Baggioli for valuable comments, as well as Gabriel Cuomo, Angelo Esposito, and the other organizers and participants of the 2022 Pollica Summer Workshop on Effective Field Theory for stimulating discussions. IK, AN and KP were supported in part by the US DOE (award number DE-SC011941) and by the Simons Foundation (award number 658906). ML was supported in part by the ALFA foundation.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2305.11226
Rights and permissions
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.
About this article
Cite this article
Kourkoulou, I., Landry, M.J., Nicolis, A. et al. Apparently superluminal superfluids. J. High Energ. Phys. 2024, 80 (2024). https://doi.org/10.1007/JHEP01(2024)080
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2024)080