Abstract
We propose an effective action that describes a relativistic fluid with Hall viscosity. The construction involves a Wess-Zumino-Witten term that exists only in (2+1) spacetime dimensions. We note that this formalism can accommodate only a Hall viscosity which is a homogeneous function of the entropy and particle number densities of degree one.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.E. Avron, R. Seiler and P.G. Zograf, Viscosity of quantum Hall fluids, Phys. Rev. Lett. 75 (1995) 697 [INSPIRE].
D.T. Son and C. Wu, Holographic Spontaneous Parity Breaking and Emergent Hall Viscosity and Angular Momentum, JHEP 07 (2014) 076 [arXiv:1311.4882] [INSPIRE].
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev. D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE].
A. Nicolis and D.T. Son, Hall viscosity from effective field theory, arXiv:1103.2137 [INSPIRE].
F.M. Haehl and M. Rangamani, Comments on Hall transport from effective actions, JHEP 10 (2013) 074 [arXiv:1305.6968] [INSPIRE].
J. Maciejko, B. Hsu, S.A. Kivelson, Y. Park and S.L. Sondhi, Field theory of the quantum Hall nematic transition, Phys. Rev. B 88 (2013) 125137 [arXiv:1303.3041] [INSPIRE].
E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].
B. Bradlyn, M. Goldstein and N. Read, Kubo formulas for viscosity: Hall viscosity, Ward identities and the relation with conductivity, Phys. Rev. B 86 (2012) 245309 [arXiv:1207.7021] [INSPIRE].
J.L. Friedman, Generic instability of rotating relativistic stars, Commun. Math. Phys. 62 (1978) 247 [INSPIRE].
S.R. Green, J.S. Schiffrin and R.M. Wald, Dynamic and Thermodynamic Stability of Relativistic, Perfect Fluid Stars, Class. Quant. Grav. 31 (2014) 035023 [arXiv:1309.0177] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Effective actions for anomalous hydrodynamics, JHEP 03 (2014) 034 [arXiv:1312.0610] [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: 1402.1146
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
Geracie, M., Son, D.T. Effective field theory for fluids: Hall viscosity from a Wess-Zumino-Witten term. J. High Energ. Phys. 2014, 4 (2014). https://doi.org/10.1007/JHEP11(2014)004
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2014)004