Geodesic
Zero-viscosity limit in a holographic Gauss–Bonnet liquid
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 76-90 Cet article a éte moissonné depuis la source Math-Net.Ru

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In recent papers, it was hypothesized that there exist dissipationless quantum liquids, i.e., liquids with zero or vanishingly small viscosity and zero entropy production, which nevertheless have nontrivial second-order transport coefficients. A natural candidate for a dissipationless liquid is the hypothetical conformal quantum liquid, whose holographically dual description in the infrared limit is given by the five-dimensional Gauss–Bonnet gravity. It is known that shear viscosity in that theory can be made arbitrarily small as the Gauss–Bonnet coupling parameter approaches a critical value. We evaluate the transport coefficients of a Gauss–Bonnet liquid (nonperturbatively in the coupling parameter; three of the six coefficients were previously unknown) and consider the zero-viscosity limit. We show that three of the five second-order coefficients are nonzero in this limit, but they do not satisfy the criterion of zero entropy production. Hence, the holographic Gauss–Bonnet liquid is not a dissipationless quantum liquid.
Keywords: gauge–gravitational duality, hydrodynamics, viscosity.
Mots-clés : Gauss–Bonnet gravity, transport coefficient 
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S. Grozdanov; A. O. Starinetz. Zero-viscosity limit in a holographic Gauss–Bonnet liquid. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 76-90. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a3/

[1] J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, U. A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv: 1101.0618

[2] D. T. Son, A. O. Starinets, Ann. Rev. Nucl. Part. Sci., 57:1 (2007), 95–118, arXiv: 0704.0240 | DOI | MR

[3] R. Baier, P. Romatschke, D. T. Son, A. O. Starinets, M. A. Stephanov, JHEP, 04 (2008), 100, 31 pp., arXiv: 0712.2451 | DOI | MR

[4] M. Rangamani, Class. Quantum Grav., 26:22 (2009), 224003, 48 pp., arXiv: 0905.4352 | DOI | MR | Zbl

[5] P. Kovtun, D. T. Son, A. O. Starinets, Phys. Rev. Lett., 94:11 (2005), 111601, 8 pp., arXiv: hep-th/0405231 | DOI

[6] A. Buchel, Phys. Lett. B, 609:3–4 (2005), 392–401, arXiv: hep-th/0408095 | DOI | MR | Zbl

[7] P. Kovtun, D. T. Son, A. O. Starinets, JHEP, 10 (2003), 064, 27 pp., arXiv: hep-th/0309213 | DOI | MR

[8] A. Buchel, J. T. Liu, Phys. Rev. Lett., 93:9 (2004), 090602, 14 pp., arXiv: hep-th/0311175 | DOI | MR

[9] A. O. Starinets, Phys. Lett. B, 670:3–4 (2009), 442–445, arXiv: 0806.3797 | DOI | MR

[10] L. D. Landau, E. M. Lifshits, Kurs teoreticheskoi fiziki, v. 6, Gidrodinamika, Nauka, M., 1986 | MR | MR

[11] P. Romatschke, Internat. J. Modern Phys. E, 19:1 (2010), 1–53, arXiv: 0902.3663 | DOI

[12] G. Policastro, D. T. Son, A. O. Starinets, Phys. Rev. Lett., 87:8 (2001), 081601, 4 pp., arXiv: hep-th/0104066 | DOI

[13] A. Buchel, J. T. Liu, A. O. Starinets, Nucl. Phys. B, 707:1–2 (2005), 56–68, arXiv: hep-th/0406264 | DOI | MR | Zbl

[14] A. Buchel, Nucl. Phys. B, 803:1–2 (2008), 166–170, arXiv: 0805.2683 | DOI | MR | Zbl

[15] S. Bhattacharyya, V. E. Hubeny, S. Minwalla, M. Rangamani, JHEP, 02 (2008), 045, 39 pp., arXiv: 0712.2456 | DOI

[16] P. Benincasa, A. Buchel, JHEP, 01 (2006), 103, 19 pp., arXiv: hep-th/0510041 | DOI | MR

[17] A. Buchel, Nucl. Phys. B, 802:3 (2008), 281–306, arXiv: 0801.4421 | DOI | MR | Zbl

[18] A. Buchel, M. Paulos, Nucl. Phys. B, 805:1–2 (2008), 59–71, arXiv: 0806.0788 | DOI | MR | Zbl

[19] A. Buchel, M. Paulos, Nucl. Phys. B, 810:1–2 (2009), 40–65, arXiv: 0808.1601 | DOI | MR | Zbl

[20] O. Saremi, K. A. Sohrabi, JHEP, 11 (2011), 147, 14 pp., arXiv: 1105.4870 | DOI | MR | Zbl

[21] S. Grozdanov, A. Starinets, Second-order transport coefficients and dissipationless liquids (to appear)

[22] S. C. Huot, S. Jeon, G. D. Moore, Phys. Rev. Lett., 98:17 (2007), 172303, 4 pp., arXiv: hep-ph/0608062 | DOI

[23] Y. Kats, P. Petrov, JHEP, 01 (2009), 044, 15 pp., arXiv: 0712.0743 | DOI | MR

[24] M. Brigante, H. Liu, R. C. Myers, S. Shenker, S. Yaida, Phys. Rev. D, 77:12 (2008), 126006, 17 pp., arXiv: arXiv:0712.0805 | DOI

[25] M. Brigante, H. Liu, R. C. Myers, S. Shenker, S. Yaida, Phys. Rev. Lett., 100:19 (2008), 191601, 5 pp., arXiv: 0802.3318 | DOI

[26] A. Buchel, S. Cremonini, JHEP, 10 (2010), 026, 4 pp., arXiv: 1007.2963 | DOI | Zbl

[27] N. Banerjee, S. Dutta, Holographic hydrodynamics: models and methods, arXiv: 1112.5345

[28] A. Buchel, R. C. Myers, JHEP, 08 (2009), 016, 19 pp., arXiv: 0906.2922 | DOI | MR

[29] E. Shaverin, A. Yarom, JHEP, 04 (2013), 013, 10 pp., arXiv: 1211.1979 | DOI | MR

[30] J. Bhattacharya, S. Bhattacharyya, M. Rangamani, JHEP, 02 (2013), 153, 27 pp., arXiv: 1211.1020 | DOI | MR

[31] A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, M. Smolkin, JHEP, 03 (2010), 111, arXiv: 0911.4257 | DOI

[32] D. T. Son, A. O. Starinets, JHEP, 09 (2002), 042, 24 pp., arXiv: hep-th/0205051 | DOI | MR

[33] G. Policastro, D. T. Son, A. O. Starinets, JHEP, 09 (2002), 043, 16 pp., arXiv: hep-th/0205052 | DOI | MR

[34] P. K. Kovtun, A. O. Starinets, Phys. Rev. D, 72:8 (2005), 086009, 16 pp., arXiv: hep-th/0506184 | DOI | MR

[35] N. Iqbal, H. Liu, Phys. Rev. D, 79:2 (2009), 025023, 15 pp., arXiv: 0809.3808 | DOI

[36] G. D. Moore, K. A. Sohrabi, Phys. Rev. Lett., 106:12 (2011), 122302, 4 pp., arXiv: 1007.5333 | DOI

[37] J. S. Schwinger, J. Math. Phys., 2:3 (1961), 407–432 | DOI | MR | Zbl

[38] L. V. Keldysh, ZhETF, 47 (1964), 1515–1527 | MR

[39] E. Wang, U. W. Heinz, Phys. Rev. D, 66:2 (2002), 025008, 17 pp., arXiv: hep-th/9809016 | DOI

[40] V. Balasubramanian, P. Kraus, Commun. Math. Phys., 208:2 (1999), 413–428, arXiv: hep-th/9902121 | DOI | MR | Zbl