Abstract
We study dissipation in holographic superfluids at finite temperature and zero chemical potential. The zero overlap with the heat current allows us to isolate the physics of the conserved current corresponding to the broken global U(1). By using analytic techniques we write constitutive relations including the first non-trivial dissipative terms. The corresponding transport coefficients are determined in terms of thermodynamic quantities and the black hole horizon data. By analysing their behaviour close to the phase transition we show explicitly the breakdown of the hydrodynamic expansion. Finally, we study the pseudo-Goldstone mode that emerges upon introducing a perturbative symmetry breaking source and we determine its resonant frequency and decay rate.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
L. Landau, Theory of the superfluidity of helium II, Phys. Rev. 60 (1941) 356.
L. Tisza, The Theory of Liquid Helium, Phys. Rev. 72 (1947) 838 [INSPIRE].
I. Khalatnikov and V. Lebedev, Relativistic hydrodynamics of a superfluid liquid, Phys. Lett. A 91 (1982) 70.
W. Israel, Covariant superfluid mechanics, Phys. Lett. A 86 (1981) 79.
J. Bhattacharya, S. Bhattacharyya and S. Minwalla, Dissipative Superfluid dynamics from gravity, JHEP 04 (2011) 125 [arXiv:1101.3332] [INSPIRE].
R.A. Davison, L.V. Delacrétaz, B. Goutéraux and S.A. Hartnoll, Hydrodynamic theory of quantum fluctuating superconductivity, Phys. Rev. B 94 (2016) 054502 [Erratum ibid. 96 (2017) 059902] [arXiv:1602.08171] [INSPIRE].
C. Crnkovic and E. Witten, Covariant description of canonical formalism in geometrical theories, (1986) http://cds.cern.ch/record/172498.
T. Andrade and A. Krikun, Commensurability effects in holographic homogeneous lattices, JHEP 05 (2016) 039 [arXiv:1512.02465] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Universal relaxation in a holographic metal lic density wave phase, Phys. Rev. Lett. 123 (2019) 211602 [arXiv:1812.08118] [INSPIRE].
A. Donos, D. Martin, C. Pantelidou and V. Ziogas, Incoherent hydrodynamics and density waves, Class. Quant. Grav. 37 (2020) 045005 [arXiv:1906.03132] [INSPIRE].
A. Donos, D. Martin, C. Pantelidou and V. Ziogas, Hydrodynamics of broken global symmetries in the bulk, JHEP 10 (2019) 218 [arXiv:1905.00398] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
O. Saremi, Shear waves, sound waves on a shimmering horizon, hep-th/0703170 [INSPIRE].
N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].
K. Damle and S. Sachdev, Nonzero-temperature transport near quantum critical points, Phys. Rev. B 56 (1997) 8714 [cond-mat/9705206] [INSPIRE].
S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
M.J. Bhaseen, J.P. Gauntlett, B.D. Simons, J. Sonner and T. Wiseman, Holographic Superfluids and the Dynamics of Symmetry Breaking, Phys. Rev. Lett. 110 (2013) 015301 [arXiv:1207.4194] [INSPIRE].
B. Goutéraux and E. Mefford, Normal charge densities in quantum critical superfluids, Phys. Rev. Lett. 124 (2020) 161604 [arXiv:1912.08849] [INSPIRE].
A. Donos, P. Kailidis and C. Pantelidou, Dissipation in inhomogeneous holographic superfluids, work in progress.
S. Grozdanov, P.K. Kovtun, A.O. Starinets and P. Tadić, The complex life of hydrodynamic modes, JHEP 11 (2019) 097 [arXiv:1904.12862] [INSPIRE].
S. Grozdanov, P.K. Kovtun, A.O. Starinets and P. Tadić, Convergence of the Gradient Expansion in Hydrodynamics, Phys. Rev. Lett. 122 (2019) 251601 [arXiv:1904.01018] [INSPIRE].
B. Withers, Short-lived modes from hydrodynamic dispersion relations, JHEP 06 (2018) 059 [arXiv:1803.08058] [INSPIRE].
A. Donos, J.P. Gauntlett and C. Pantelidou, Holographic Abrikosov Lattices, JHEP 07 (2020) 095 [arXiv:2001.11510] [INSPIRE].
S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett. B 683 (2010) 201 [arXiv:0908.0011] [INSPIRE].
B. Goutéraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP 04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
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: 2107.03680
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
Donos, A., Kailidis, P. & Pantelidou, C. Dissipation in holographic superfluids. J. High Energ. Phys. 2021, 134 (2021). https://doi.org/10.1007/JHEP09(2021)134
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2021)134