×

zbMATH — the first resource for mathematics

Topological sigma models & dissipative hydrodynamics. (English) Zbl 1388.83351
Summary: We outline a universal Schwinger-Keldysh effective theory which describes macroscopic thermal fluctuations of a relativistic field theory. The basic ingredients of our construction are three: a doubling of degrees of freedom, an emergent abelian symmetry associated with entropy, and a topological (BRST) supersymmetry imposing fluctuation-dissipation theorem. We illustrate these ideas for a non-linear viscous fluid, and demonstrate that the resulting effective action obeys a generalized fluctuation-dissipation theorem, which guarantees a local form of the second law.

MSC:
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Schwinger, JS, Brownian motion of a quantum oscillator, J. Math. Phys., 2, 407, (1961) · Zbl 0098.43503
[2] L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz.47 (1964) 1515 [Sov. Phys. JETP20 (1965) 1018] [INSPIRE].
[3] Feynman, RP; Vernon, FL, The theory of a general quantum system interacting with a linear dissipative system, Annals Phys., 24, 118, (1963)
[4] L.D. Landau and E.M. Lifshitz, Course of theoretical physics, vol. 6, Butterworth-Heinemann, U.K. (1987).
[5] Rangamani, M., Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav., 26, 224003, (2009) · Zbl 1181.83005
[6] 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]. · Zbl 1263.83009
[7] Bhattacharyya, S., Constraints on the second order transport coefficients of an uncharged fluid, JHEP, 07, 104, (2012)
[8] Banerjee, N.; Bhattacharya, J.; Bhattacharyya, S.; Jain, S.; Minwalla, S.; Sharma, T., Constraints on fluid dynamics from equilibrium partition functions, JHEP, 09, 046, (2012) · Zbl 1397.82026
[9] Jensen, K.; Kaminski, M.; Kovtun, P.; Meyer, R.; Ritz, A.; Yarom, A., Towards hydrodynamics without an entropy current, Phys. Rev. Lett., 109, 101601, (2012)
[10] Bhattacharyya, S., Entropy current and equilibrium partition function in fluid dynamics, JHEP, 08, 165, (2014) · Zbl 1333.81066
[11] Bhattacharyya, S., Entropy current from partition function: one example, JHEP, 07, 139, (2014)
[12] Haehl, FM; Loganayagam, R.; Rangamani, M., The eightfold way to dissipation, Phys. Rev. Lett., 114, 201601, (2015) · Zbl 1388.81456
[13] Haehl, FM; Loganayagam, R.; Rangamani, M., Adiabatic hydrodynamics: the eightfold way to dissipation, JHEP, 05, 060, (2015) · Zbl 1388.81456
[14] Nickel, D.; Son, DT, Deconstructing holographic liquids, New J. Phys., 13, 075010, (2011)
[15] Dubovsky, S.; Hui, L.; Nicolis, A.; Son, DT, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev., D 85, 085029, (2012)
[16] Dubovsky, S.; Hui, L.; Nicolis, A., Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, Phys. Rev., D 89, 045016, (2014)
[17] Endlich, S.; Nicolis, A.; Porto, RA; Wang, J., Dissipation in the effective field theory for hydrodynamics: first order effects, Phys. Rev., D 88, 105001, (2013)
[18] Haehl, FM; Loganayagam, R.; Rangamani, M., Effective actions for anomalous hydrodynamics, JHEP, 03, 034, (2014)
[19] Grozdanov, S.; Polonyi, J., Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev., D 91, 105031, (2015)
[20] Kovtun, P.; Moore, GD; Romatschke, P., Towards an effective action for relativistic dissipative hydrodynamics, JHEP, 07, 123, (2014)
[21] Grozdanov, S.; Polonyi, J., Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasiparticles, Phys. Rev., D 92, 065009, (2015)
[22] Harder, M.; Kovtun, P.; Ritz, A., On thermal fluctuations and the generating functional in relativistic hydrodynamics, JHEP, 07, 025, (2015) · Zbl 1388.83352
[23] Crossley, M.; Glorioso, P.; Liu, H.; Wang, Y., Off-shell hydrodynamics from holography, JHEP, 02, 124, (2016) · Zbl 1388.83344
[24] Boer, J.; Heller, MP; Pinzani-Fokeeva, N., Effective actions for relativistic fluids from holography, JHEP, 08, 086, (2015) · Zbl 1388.83360
[25] Bertini, L.; Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C., Macroscopic fluctuation theory, Rev. Mod. Phys., 87, 593, (2015) · Zbl 1031.82038
[26] Papadodimas, K.; Raju, S., An infalling observer in AdS/CFT, JHEP, 10, 212, (2013)
[27] Bhattacharyya, S.; Hubeny, VE; Minwalla, S.; Rangamani, M., Nonlinear fluid dynamics from gravity, JHEP, 02, 045, (2008)
[28] L. Susskind and E. Witten, The holographic bound in anti-de Sitter space, hep-th/9805114 [INSPIRE].
[29] G. ’t Hooft and M.J.G. Veltman, Diagrammar, NATO Sci. Ser.B 4 (1974) 177 [INSPIRE].
[30] Martin, PC; Siggia, ED; Rose, HA, Statistical dynamics of classical systems, Phys. Rev., A 8, 423, (1973)
[31] Zinn-Justin, J., Quantum field theory and critical phenomena, Int. Ser. Monogr. Phys., 113, 1, (2002)
[32] Haehl, FM; Loganayagam, R.; Rangamani, M., The fluid manifesto: emergent symmetries, hydrodynamics and black holes, JHEP, 01, 184, (2016) · Zbl 1388.83350
[33] Vafa, C.; Witten, E., A strong coupling test of S duality, Nucl. Phys., B 431, 3, (1994) · Zbl 0964.81522
[34] Dijkgraaf, R.; Moore, GW, Balanced topological field theories, Commun. Math. Phys., 185, 411, (1997) · Zbl 0888.58008
[35] C. Jarzynski, Nonequilibrium equality for free energy differences, Phys. Rev. Lett.78 (1997) 2690 [cond-mat/9610209].
[36] C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: a master-equation approach, Phys. Rev.E 56 (1997) 5018 [cond-mat/9707325].
[37] Crooks, GE, Nonequilibrium measurements of free energy differences for microscopically reversible Markovian systems, J. Stat. Phys., 90, 1481, (1998) · Zbl 0946.82029
[38] Crooks, GE, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev., E 60, 2721, (1999)
[39] Mallick, K.; Moshe, M.; Orland, H., A field-theoretic approach to nonequilibrium work identities, J. Phys., A 44, 095002, (2011) · Zbl 1211.82044
[40] Gaspard, P., Fluctuation relations for equilibrium states with broken discrete symmetries, J. Stat. Mech., 8, 08021, (2012)
[41] Gaspard, P., Time-reversal symmetry relations for fluctuating currents in nonequilibrium systems, Acta Phys. Polon., B 44, 815, (2013) · Zbl 1371.82087
[42] F.M. Haehl, R. Loganayagam and M. Rangamani, Equivariant construction of dissipative dynamics, to appear (2015). · Zbl 1388.83351
[43] M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, arXiv:1511.03646 [INSPIRE]. · Zbl 1382.81199
[44] Horne, JH, Superspace versions of topological theories, Nucl. Phys., B 318, 22, (1989)
[45] 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].
[46] P.C. Martin and J.S. Schwinger, Theory of many particle systems. 1, Phys. Rev.115 (1959) 1342 [INSPIRE].
[47] Haag, R.; Hugenholtz, NM; Winnink, M., On the equilibrium states in quantum statistical mechanics, Commun. Math. Phys., 5, 215, (1967) · Zbl 0171.47102
[48] R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev.D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE]. · Zbl 0942.83512
[49] 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].
[50] Onsager, L., Reciprocal relations in irreversible processes. I, Phys. Rev., 37, 405, (1931) · JFM 57.1168.10
[51] Onsager, L., Reciprocal relations in irreversible processes. II, Phys. Rev., 38, 2265, (1931) · Zbl 0004.18303
[52] Baier, R.; Romatschke, P.; Son, DT; Starinets, AO; Stephanov, MA, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP, 04, 100, (2008) · Zbl 1246.81352
[53] Loganayagam, R., Entropy current in conformal hydrodynamics, JHEP, 05, 087, (2008)
[54] Policastro, G.; Son, DT; Starinets, AO, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett., 87, 081601, (2001)
[55] Haack, M.; Yarom, A., Universality of second order transport coefficients from thegauge-string duality, Nucl. Phys., B 813, 140, (2009) · Zbl 1194.81207
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.