Abstract
In this paper we further develop the fluctuating hydrodynamics proposed in [1] in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a Z 2 symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, arXiv:1511.03646 [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].
S. Endlich, A. Nicolis, R.A. Porto and J. Wang, Dissipation in the effective field theory for hydrodynamics: First order effects, Phys. Rev. D 88 (2013) 105001 [arXiv:1211.6461] [INSPIRE].
S. Dubovsky, L. Hui and A. Nicolis, Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, Phys. Rev. D 89 (2014) 045016 [arXiv:1107.0732] [INSPIRE].
S. Endlich, A. Nicolis, R. Rattazzi and J. Wang, The Quantum mechanics of perfect fluids, JHEP 04 (2011) 102 [arXiv:1011.6396] [INSPIRE].
A. Nicolis and D.T. Son, Hall viscosity from effective field theory, arXiv:1103.2137 [INSPIRE].
A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids, arXiv:1108.2513 [INSPIRE].
L.V. Delacrétaz, A. Nicolis, R. Penco and R.A. Rosen, Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids and Supersolids, Phys. Rev. Lett. 114 (2015) 091601 [arXiv:1403.6509] [INSPIRE].
M. Geracie and D.T. Son, Effective field theory for fluids: Hall viscosity from a Wess-Zumino-Witten term, JHEP 11 (2014) 004 [arXiv:1402.1146] [INSPIRE].
S. Grozdanov and J. Polonyi, Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev. D 91 (2015) 105031 [arXiv:1305.3670] [INSPIRE].
M. Harder, P. Kovtun and A. Ritz, On thermal fluctuations and the generating functional in relativistic hydrodynamics, JHEP 07 (2015) 025 [arXiv:1502.03076] [INSPIRE].
P. Kovtun, G.D. Moore and P. Romatschke, Towards an effective action for relativistic dissipative hydrodynamics, JHEP 07 (2014) 123 [arXiv:1405.3967] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The eightfold way to dissipation, Phys. Rev. Lett. 114 (2015) 201601 [arXiv:1412.1090] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabatic hydrodynamics: The eightfold way to dissipation, JHEP 05 (2015) 060 [arXiv:1502.00636] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, The Fluid Manifesto: Emergent symmetries, hydrodynamics and black holes, JHEP 01 (2016) 184 [arXiv:1510.02494] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Topological σ-models & dissipative hydrodynamics, JHEP 04 (2016) 039 [arXiv:1511.07809] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace, JHEP 06 (2017) 069 [arXiv:1610.01940] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology, JHEP 06 (2017) 070 [arXiv:1610.01941] [INSPIRE].
N. Andersson and G.L. Comer, A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics, Class. Quant. Grav. 32 (2015) 075008 [arXiv:1306.3345] [INSPIRE].
S. Floerchinger, Variational principle for theories with dissipation from analytic continuation, JHEP 09 (2016) 099 [arXiv:1603.07148] [INSPIRE].
D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].
J. de Boer, M.P. Heller and N. Pinzani-Fokeeva, Effective actions for relativistic fluids from holography, JHEP 08 (2015) 086 [arXiv:1504.07616] [INSPIRE].
M. Crossley, P. Glorioso, H. Liu and Y. Wang, Off-shell hydrodynamics from holography, JHEP 02 (2016) 124 [arXiv:1504.07611] [INSPIRE].
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford U.K. (2002).
P. Gao and H. Liu, Emergent Supersymmetry in Local Equilibrium Systems, arXiv:1701.07445 [INSPIRE].
K. Jensen, N. Pinzani-Fokeeva and A. Yarom, Dissipative hydrodynamics in superspace, arXiv:1701.07436 [INSPIRE].
P. Glorioso and H. Liu, The second law of thermodynamics from symmetry and unitarity, arXiv:1612.07705 [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla and T. Sharma, Constraints on Fluid Dynamics from Equilibrium Partition Functions, JHEP 09 (2012) 046 [arXiv:1203.3544] [INSPIRE].
K. Jensen, M. Kaminski, P. Kovtun, R. Meyer, A. Ritz and A. Yarom, Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
M. Haack and A. Yarom, Universality of second order transport coefficients from the gauge-string duality, Nucl. Phys. B 813 (2009) 140 [arXiv:0811.1794] [INSPIRE].
E. Shaverin and A. Yarom, Universality of second order transport in Gauss-Bonnet gravity, JHEP 04 (2013) 013 [arXiv:1211.1979] [INSPIRE].
S. Grozdanov and A.O. Starinets, On the universal identity in second order hydrodynamics, JHEP 03 (2015) 007 [arXiv:1412.5685] [INSPIRE].
S. Grozdanov and A.O. Starinets, Zero-viscosity limit in a holographic Gauss-Bonnet liquid, Theor. Math. Phys. 182 (2015) 61 [Teor. Mat. Fiz. 182 (2014) 76].
E. Shaverin, A breakdown of a universal hydrodynamic relation in Gauss-Bonnet gravity, arXiv:1509.05418 [INSPIRE].
P. Romatschke, Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy, Class. Quant. Grav. 27 (2010) 025006 [arXiv:0906.4787] [INSPIRE].
S. Bhattacharyya, Constraints on the second order transport coefficients of an uncharged fluid, JHEP 07 (2012) 104 [arXiv:1201.4654] [INSPIRE].
S. Bhattacharyya, Entropy Current from Partition Function: One Example, JHEP 07 (2014) 139 [arXiv:1403.7639] [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: 1701.07817
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
Glorioso, P., Crossley, M. & Liu, H. Effective field theory of dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current. J. High Energ. Phys. 2017, 96 (2017). https://doi.org/10.1007/JHEP09(2017)096
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2017)096