Abstract
We focus on the question of how relativistic fluid dynamics should be thought of as a Wilsonian effective field theory emerging from Schwinger-Keldysh path integrals. Taking the basic principles of Schwinger-Keldysh formalism seriously, we are led to a series of remarkable statements and conjectures, which we phrase in terms of a broad programme relating relativistic fluid dynamics and topological sigma models. Apart from the intrinsic interest for these ideas from the non-equilibrium field theory viewpoint, we also emphasize its relevance to various fundamental questions in black hole physics.
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References
J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2 (1961) 407 [INSPIRE].
L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47 (1964) 1515 [Sov. Phys. JETP 20 (1965) 1018] [INSPIRE].
L.D. Landau and E.M. Lifshitz, Course of theoretical physics, vol. 6, Butterworth-Heinemann, U.K. (1987).
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].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
W. Israel, Thermo field dynamics of black holes, Phys. Lett. A 57 (1976) 107 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [INSPIRE].
K. Skenderis and B.C. van Rees, Real-time gauge/gravity duality: prescription, renormalization and examples, JHEP 05 (2009) 085 [arXiv:0812.2909] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear fluid dynamics from gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, in Black holes in higher dimensions, (2012), pg. 348 [arXiv:1107.5780] [INSPIRE].
K.-C. Chou, Z.-B. Su, B.-L. Hao and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rept. 118 (1985) 1 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Diagrammar, NATO Sci. Ser. B 4 (1974) 177 [INSPIRE].
E. Witten, Supersymmetry and Morse theory, J. Diff. Geom. 17 (1982) 661 [INSPIRE].
G. Evenbly and G. Vidal, Tensor network renormalization, Phys. Rev. Lett. 115 (2015) 180405 [arXiv:1412.0732].
J. Alfaro and P.H. Damgaard, BRST symmetry of field redefinitions, Annals Phys. 220 (1992) 188 [INSPIRE].
D. Birmingham, M. Blau, M. Rakowski and G. Thompson, Topological field theory, Phys. Rept. 209 (1991) 129 [INSPIRE].
R. Kubo, Statistical mechanical theory of irreversible processes. 1. General theory and simple applications in magnetic and conduction problems, J. Phys. Soc. Jap. 12 (1957) 570 [INSPIRE].
P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1, Phys. Rev. 115 (1959) 1342 [INSPIRE].
H.A. Weldon, Two sum rules for the thermal n-point functions, Phys. Rev. D 72 (2005) 117901 [INSPIRE].
S. Cecotti and C. Vafa, 2d wall-crossing, R-twisting and a supersymmetric index, arXiv:1002.3638 [INSPIRE].
R. Dijkgraaf and G.W. Moore, Balanced topological field theories, Commun. Math. Phys. 185 (1997) 411 [hep-th/9608169] [INSPIRE].
C. Vafa and E. Witten, A strong coupling test of S duality, Nucl. Phys. B 431 (1994) 3 [hep-th/9408074] [INSPIRE].
R. Zucchini, Basic and equivariant cohomology in balanced topological field theory, J. Geom. Phys. 35 (2000) 299 [hep-th/9804043] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Equivariant construction of dissipative dynamics, to appear (2015).
K. Jensen, R. Loganayagam and A. Yarom, Anomaly inflow and thermal equilibrium, JHEP 05 (2014) 134 [arXiv:1310.7024] [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Effective actions for anomalous hydrodynamics, JHEP 03 (2014) 034 [arXiv:1312.0610] [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].
E. Witten, Analytic continuation of Chern-Simons theory, AMS/IP Stud. Adv. Math. 50 (2011) 347 [arXiv:1001.2933] [INSPIRE].
N. Marcus, The other topological twisting of N = 4 Yang-Mills, Nucl. Phys. B 452 (1995) 331 [hep-th/9506002] [INSPIRE].
A. Kapustin and E. Witten, Electric-magnetic duality and the geometric Langlands program, Commun. Num. Theor. Phys. 1 (2007) 1 [hep-th/0604151] [INSPIRE].
V. Mathai and D.G. Quillen, Superconnections, Thom classes and equivariant differential forms, Topology 25 (1986) 85 [INSPIRE].
P.C. Martin, E.D. Siggia and H.A. Rose, Statistical dynamics of classical systems, Phys. Rev. A 8 (1973) 423 [INSPIRE].
F.M. Haehl, R. Loganayagam and M. Rangamani, Adiabaticity, dissipation, and KMS flavour invariance, work in progress (2015).
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. 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].
J. Bhattacharya, S. Bhattacharyya and M. Rangamani, Non-dissipative hydrodynamics: effective actions versus entropy current, JHEP 02 (2013) 153 [arXiv:1211.1020] [INSPIRE].
S. Grozdanov and J. Polonyi, Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev. D 91 (2015) 105031 [arXiv:1305.3670] [INSPIRE].
S. Grozdanov and J. Polonyi, Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasiparticles, Phys. Rev. D 92 (2015) 065009 [arXiv:1501.06620] [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].
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].
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, arXiv:1504.07611 [INSPIRE].
D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys. 13 (2011) 075010 [arXiv:1009.3094] [INSPIRE].
K. Jensen, R. Loganayagam and A. Yarom, Chern-Simons terms from thermal circles and anomalies, JHEP 05 (2014) 110 [arXiv:1311.2935] [INSPIRE].
F. Ferrari, Gauge theories, D-branes and holography, Nucl. Phys. B 880 (2014) 247 [arXiv:1310.6788] [INSPIRE].
S.R. Das, G. Mandal and S.R. Wadia, Stochastic quantization on two-dimensional theory space and Morse theory, Mod. Phys. Lett. A 4 (1989) 745 [INSPIRE].
G. Parisi and N. Sourlas, Random magnetic fields, supersymmetry and negative dimensions, Phys. Rev. Lett. 43 (1979) 744 [INSPIRE].
C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett. 78 (1997) 2690 [cond-mat/9610209].
C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: a master-equation approach, Phys. Rev. E 56 (1997) 5018 [cond-mat/9707325].
K. Papadodimas and S. Raju, An infalling observer in AdS/CFT, JHEP 10 (2013) 212 [arXiv:1211.6767] [INSPIRE].
K. Papadodimas and S. Raju, Black hole interior in the holographic correspondence and the information paradox, Phys. Rev. Lett. 112 (2014) 051301 [arXiv:1310.6334] [INSPIRE].
K. Papadodimas and S. Raju, Comments on the necessity and implications of state-dependence in the black hole interior, arXiv:1503.08825 [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
L. Susskind, Some speculations about black hole entropy in string theory, hep-th/9309145 [INSPIRE].
J. de Boer, V.E. Hubeny, M. Rangamani and M. Shigemori, Brownian motion in AdS/CFT, JHEP 07 (2009) 094 [arXiv:0812.5112] [INSPIRE].
D.T. Son and D. Teaney, Thermal noise and stochastic strings in AdS/CFT, JHEP 07 (2009) 021 [arXiv:0901.2338] [INSPIRE].
J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys. 61 (2013) 781 [arXiv:1306.0533] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
K. Efetov, Supersymmetry in disorder and chaos, Cambridge University Press, Cambridge U.K. (1999).
J. Kurchan, Supersymmetry, replica and dynamic treatments of disordered systems: a parallel presentation, cond-mat/0209399.
H. Ooguri, A. Strominger and C. Vafa, Black hole attractors and the topological string, Phys. Rev. D 70 (2004) 106007 [hep-th/0405146] [INSPIRE].
J. Zinn-Justin, Quantum field theory and critical phenomena, Int. Ser. Monogr. Phys. 113 (2002) 1 [INSPIRE].
H.-K. Janssen, On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties, Z. Phys. B 23 (1976) 377.
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].
J.H. Horne, Superspace versions of topological theories, Nucl. Phys. B 318 (1989) 22 [INSPIRE].
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ArXiv ePrint: 1510.02494
This short note summarizes two talks at Strings 2015, Bengaluru, by two of the authors.
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Haehl, F.M., Loganayagam, R. & Rangamani, M. The fluid manifesto: emergent symmetries, hydrodynamics, and black holes. J. High Energ. Phys. 2016, 184 (2016). https://doi.org/10.1007/JHEP01(2016)184
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DOI: https://doi.org/10.1007/JHEP01(2016)184