Abstract
We propose an effective action for first order relativistic dissipative hydrodynamics that can be used to evaluate n-point symmetrized correlation functions, taking into account thermal fluctuations of the hydrodynamic variables.
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L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Pergamon (1987).
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
Y. Pomeau and P. Résibois, Time dependent correlation functions and mode-mode coupling theories, Phys. Rept. 19 (1975) 63.
L.D. Landau and E.M. Lifshitz, Hydrodynamic fluctuations, JETP 32 (1957) 618 [Sov. Phys. JETP 5 (1957) 512].
D. Förster, D.R. Nelson and M.J. Stephen, Large-distance and long-time properties of a randomly stirred fluid, Phys. Rev. A 16 (1977) 732 [INSPIRE].
C. De Dominicis and L. Peliti, Field Theory Renormalization and Critical Dynamics Above T c : Helium, Antiferromagnets and Liquid Gas Systems, Phys. Rev. B 18 (1978) 353 [INSPIRE].
B.F. Schutz, Perfect Fluids in General Relativity: Velocity Potentials and a Variational Principle, Phys. Rev. D 2 (1970) 2762 [INSPIRE].
J.D. Brown, Action functionals for relativistic perfect fluids, Class. Quant. Grav. 10 (1993) 1579 [gr-qc/9304026] [INSPIRE].
B. Carter, Axionic vorticity variational formulation for relativistic perfect fluids, Class. Quant. Grav. 11 (1994) 2013 [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].
J. Bhattacharya, S. Bhattacharyya and M. Rangamani, Non-dissipative hydrodynamics: Effective actions versus entropy current, JHEP 02 (2013) 153 [arXiv:1211.1020] [INSPIRE].
N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Jain, S. Minwalla et al., 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 et al., Towards hydrodynamics without an entropy current, Phys. Rev. Lett. 109 (2012) 101601 [arXiv:1203.3556] [INSPIRE].
N. Andersson and G.L. Comer, Relativistic fluid dynamics: Physics for many different scales, Living Rev. Rel. 10 (2007) 1 [gr-qc/0605010] [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. Grozdanov and J. Polonyi, Viscosity and dissipative hydrodynamics from effective field theory, arXiv:1305.3670 [INSPIRE].
P. Kovtun and L.G. Yaffe, Hydrodynamic fluctuations, long time tails and supersymmetry, Phys. Rev. D 68 (2003) 025007 [hep-th/0303010] [INSPIRE].
J. Peralta-Ramos and E. Calzetta, Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics, JHEP 02 (2012) 085 [arXiv:1109.3833] [INSPIRE].
P. Kovtun, G.D. Moore and P. Romatschke, The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics, Phys. Rev. D 84 (2011) 025006 [arXiv:1104.1586] [INSPIRE].
J.I. Kapusta, B. Müller and M. Stephanov, Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions, Phys. Rev. C 85 (2012) 054906 [arXiv:1112.6405] [INSPIRE].
A. Kumar, J.R. Bhatt and A.P. Mishra, Fluctuations in Relativistic Causal Hydrodynamics, arXiv:1304.1873 [INSPIRE].
K. Murase and T. Hirano, Relativistic fluctuating hydrodynamics with memory functions and colored noises, arXiv:1304.3243 [INSPIRE].
C. Young, Numerical integration of thermal noise in relativistic hydrodynamics, arXiv:1306.0472 [INSPIRE].
E.M. Lifshitz and L.P. Pitaevskii, Statistical Physics, Part 2, Pergamon (1980).
P.B. Arnold, Symmetric path integrals for stochastic equations with multiplicative noise, Phys. Rev. E 61 (2000) 6099 [hep-ph/9912209] [INSPIRE].
J. Zanella and E. Calzetta, Renormalization group and nonequilibrium action in stochastic field theory, Phys. Rev. E 66 (2002) 036134 [cond-mat/0203566] [INSPIRE].
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Kovtun, P., Moore, G.D. & Romatschke, P. Towards an effective action for relativistic dissipative hydrodynamics. J. High Energ. Phys. 2014, 123 (2014). https://doi.org/10.1007/JHEP07(2014)123
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DOI: https://doi.org/10.1007/JHEP07(2014)123