Strongly coupled heavy and light quark thermal motion from AdS/CFT. (English) Zbl 1483.81148
Summary: We give a pedagogical presentation of heavy and light probe quarks in a thermal plasma using the AdS/CFT correspondence. Three cases are considered: external heavy and light quarks undergoing Brownian motion in the plasma, and an external heavy quark moving through the plasma with a constant velocity. For the first two cases we compute the mean-squared transverse displacement of the string’s boundary endpoint. At early times the behaviour is ballistic, while the late time dynamics are diffusive. We extract the diffusion coefficient for both heavy and light quarks in an arbitrary number of dimensions and comment on the relevance for relativistic heavy ion phenomenology.
MSC:
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81V35 | Nuclear physics |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
References:
| [1] | Aronson, A.; Ludlam, T., Hunting the Quark Gluon Plasma: Results from the First 3 Years at the Relativistic Heavy Ion Collider (RHIC)Formal Report: BNL-73847 (2005), Brookhaven National Laboratory: Brookhaven National Laboratory Upton, New York, Available at http://www.bnl.gov/npp/docs/Hunting the QGP.pdf |
| [2] | Heinz, U.; Kolb, P., Nuclear Phys. A, 702, 1-4 (2002), arXiv:hep-ph/0111075 |
| [3] | Gyulassy, M., (Structure and Dynamics of Elementary Matter (NATO Advanced Study Institute) (2004), Springer), 159-182, arXiv:nucl-th/0403032 |
| [4] | Heinz, U.; Snellings, R., Annu. Rev. Nucl. Part. Sci., 63, 1 (2013), arXiv:1301.2826 [nucl-th] |
| [5] | Gale, C.; Jeon, S.; Schenke, B., Internat. J. Modern Phys. A, 28, 11 (2013), arXiv:1301.5893 [nucl-th] |
| [6] | Majumder, A.; van Leeuwen, M., Prog. Part. Nucl. Phys., 66, 1 (2011), arXiv:1002.2206 [hep-ph] |
| [7] | Horowitz, W., Nuclear Phys. A, 904-905 (2013), arXiv:1210.8330 [nucl-th] |
| [8] | Djordjevic, M.; Djordjevic, M.; Blagojevic, B., Phys. Lett. B, 737 (2014), arXiv:1405.4250 [nucl-th] |
| [9] | Hirano, T.; Huovinen, P.; Nara, Y., Phys. Rev. C, 84, 1 (2011), arXiv:1012.3955 [nucl-th] |
| [10] | Shen, C.; Heinz, U.; Huovinen, P.; Song, H., Phys. Rev. C, 84, 4 (2011), arXiv:1105.3226 [nucl-th] |
| [11] | Qiu, Z.; Shen, C.; Heinz, U., Phys. Lett. B, 707, 1 (2012), arXiv:1110.3033 [nucl-th] |
| [12] | Gale, C.; Jeon, S.; Schenke, B.; Tribedy, P.; Venugopalan, R., Phys. Rev. Lett., 110, 1 (2013), arXiv:1209.6330 [nucl-th] |
| [13] | Gubser, S.; Klebanov, I.; Peet, A., Phys. Rev. D, 54, 6 (1996), arXiv:hep-th/9602135 |
| [14] | Casalderrey-Solana, J.; Liu, H.; Mateos, D.; Rajagopal, K.; Wiedemann, U. (2014), Cambridge University Press, arXiv:1101.0618 [hep-th] · Zbl 1325.81004 |
| [15] | Morad, R.; Horowitz, W., J. High Energy Phys., 2014, 11 (2014), arXiv:1409.75455 [hep-th] |
| [16] | Casalderrey-Solana, J.; Gulhan, D.; Milhano, J.; Pablos, D.; Rajagopal, K., J. High Energy Phys., 2014, 10 (2014), arXiv:1405.3864 [hep-ph] |
| [17] | Horowitz, W., Phys. Rev. D, 91, 8 (2015), arXiv:1501.04693 [hep-ph] |
| [18] | ’t Hooft, G., Nucl. Phys. B, 72, 3, 461-473 (1974) |
| [19] | Klebanov, I., (Strings, Branes and Gravity (2001), World Scientific), arXiv:hep-th/0009139 |
| [20] | Natsuume, M., AdS/CFT Duality User Guide, Vol. 903 (2015), Springer, arXiv:1409.3575 [hep-th] · Zbl 1350.83001 |
| [21] | Maldacena, J., Internat. J. Theoret. Phys., 38, 4, 1113-1133 (1999), arXiv:hep-th/9711200 · Zbl 0969.81047 |
| [22] | Gubser, S., Phys. Rev. D, 74, 12 (2006), arXiv:hep-th/0605182 |
| [23] | Bak, D.; Karch, A.; Yaffe, L., J. High Energy Phys., 2007, 08 (2007), arXiv:0705.0994 [hep-th] |
| [24] | Witten, E., Adv. Theor. Math. Phys., 2, 253-291 (1998), arXiv:hep-th/9802150 · Zbl 0914.53048 |
| [25] | Gubser, S.; Klebanov, I.; Polyakov, A., Phys. Lett. B, 428, 1-2, 105-114 (1998), arXiv:hep-th/9802109 · Zbl 1355.81126 |
| [26] | Aharony, O.; Witten, E., J. High Energy Phys., 1998, 11, 018 (1998), arXiv:hep-th/9807205 · Zbl 0949.81028 |
| [27] | Aharony, O.; Gubser, S.; Maldacena, J.; Ooguri, H.; Oz, Y., Phys. Rep., 323, 3-4, 183-386 (2000), arXiv:hep-th/9905111 · Zbl 1368.81009 |
| [28] | Policastro, G.; Son, D.; Starinets, A., Phys. Rev. Lett., 87, 8 (2001), arXiv:hep-th/0104066 |
| [29] | Adler, S., Phys. Rev. Lett., 91, 18 (2003), arXiv:nucl-ex/0305013 |
| [30] | Adams, J., Phys. Rev. C, 72, 1 (2005), arXiv:nucl-ex/0409033 |
| [31] | Kovtun, P.; Son, D.; Starinets, A., J. High Energy Phys., 2003, 10, 064 (2003), arXiv:hep-th/0309213 |
| [32] | Kovtun, P.; Son, D.; Starinets, A., Phys. Rev. Lett., 94, 11 (2005), arXiv:hep-th/0405231 |
| [33] | Buchel, A.; Liu, J., Phys. Rev. Lett., 93, 9 (2004), arXiv:hep-th/0311175 |
| [34] | Buchel, A., Phys. Lett. B, 609, 3-4, 392-401 (2005), arXiv:hep-th/0408095 · Zbl 1247.83220 |
| [35] | Herzog, C.; Karch, A.; Kovtun, P.; Kozcaz, C.; Yaffe, L., J. High Energy Phys., 2006, 07, 013 (2006), arXiv:hep-th/0605158 |
| [36] | Liu, H.; Rajagopal, K.; Wiedemann, U., Phys. Rev. Lett., 97, 18 (2006), arXiv:hep-ph/0605178 |
| [37] | Herzog, C., J. High Energy Phys., 2006, 09, 032 (2006), arXiv:hep-th/0605191 |
| [38] | Casalderrey-Solana, J.; Teaney, D., Phys. Rev. D, 74, 8 (2006), arXiv:hep-ph/0605199 |
| [39] | Liu, H.; Rajagopal, K.; Wiedemann, U., J. High Energy Phys., 2007, 03, 066 (2007), arXiv:hep-ph/0612168 |
| [40] | Casalderrey-Solana, J.; Teaney, D., J. High Energy Phys., 2007, 04, 039 (2007), arXiv:hep-th/0701123 |
| [41] | Gubser, S., Nuclear Phys. B, 790, 1-2, 175-199 (2008), arXiv:hep-th/061214 · Zbl 1151.81371 |
| [42] | de Boer, J.; Hubeny, V.; Rangamani, M.; Shigemori, M., J. High Energy Phys., 2009, 07, 094 (2009), arXiv:0812.5112 [hep-th] |
| [43] | Son, D.; Teaney, D., J. High Energy Phys., 2009, 07 (2009), arXiv:0901.2338 [hep-th] |
| [44] | Fischler, W.; Pedraza, J.; Tangarife Garcia, W., J. High Energy Phys., 2012, 12 (2012), arXiv:1209.1044 [hep-th] |
| [45] | Atmaja, A., J. High Energy Phys., 2013, 4 (2013), arXiv:1212.5319 [hep-th] |
| [46] | Atmaja, A.; de Boer, J.; Shigemori, M., Nuclear Phys. B, 880, 23-75 (2014), arXiv:1002.2429 [hep-th] · Zbl 1284.81289 |
| [47] | Banerjee, P.; Sathiapalan, B., Nuclear Phys. B, 884 (2014), arXiv:1308.3352 [hep-th] |
| [48] | Chakrabortty, S.; Chakraborty, S.; Haque, N., Phys. Rev. D, 89, 6 (2014), arXiv:1311.5023 [hep-th] |
| [49] | Sadeghi, J.; Pourasadollah, F.; Vaez, H., Adv. High Energy Phys., 2014 (2014), arXiv:1308.2483 [hep-th] |
| [50] | Sadeghi, J.; Pourhassan, B.; Pourasadollah, F., Eur. Phys. J. C, 74, 3 (2014), arXiv:1312.4906 [hep-th] |
| [51] | Fischler, W.; Nguyen, P.; Pedraza, J.; Tangarife, W., J. High Energy Phys., 2014, 8 (2014), arXiv:1404.0347 [hep-th] |
| [52] | Moerman, R.; Horowitz, W., A semi-classical recipe for wobbly limp noodles in partonic soup (2016), arXiv preprint arXiv:1605.09285 [hep-th] |
| [53] | Brown, R., Phil. Mag., 4, 21, 161-173 (1828) |
| [54] | Karch, A.; Katz, E., J. High Energy Phys., 2002, 06 (2002), arXiv:hep-th/0205236 |
| [55] | Polyakov, A., Nuclear Phys. B, 68, 1-3, 1-8 (1998), arXiv:hep-th/9711002 · Zbl 0999.81527 |
| [56] | ’t Hooft, G., (Salamfestschrift: A Collection of Talks, Vol. 4, no. A (1993), World Scientific), 1, arXiv:gr-qc/9310026 |
| [57] | Susskind, L., J. Math. Phys., 36, 11, 6377-6396 (1995), arXiv:hep-th/9409089 · Zbl 0850.00013 |
| [58] | Thorn, C., (Proceedings of the First International Sakharov Conference on Physics (1992)), 447-454, arXiv:hep-th/9405069 |
| [59] | Gibbons, G.; Maeda, K., Nuclear Phys. B, 298, 4, 741-775 (1988) |
| [60] | Horowitz, G.; Strominger, A., Nuclear Phys. B, 360, 1, 197-209 (1991) |
| [61] | Garfinkle, D.; Horowitz, G.; Strominger, A., Phys. Rev. D, 43, 10, 3140 (1991) |
| [62] | Ballón Bayona, C.; Braga, N., Gen. Relativity Gravitation, 39, 9 (2007), arXiv:hep-th/0512182 |
| [63] | Mateos, D., Classical Quantum Gravity, 24, 21 (2007), arXiv:0709.1523 [hep-th] |
| [64] | Witten, E., Adv. Theor. Math. Phys., 2, IASSNS-HEP-98-21, 89-117 (1998), arXiv:hep-th/9803131 |
| [65] | Douglas, M.; Taylor, D., Branes in the bulk of anti-de sitter space (1998), arXiv:hep-th/9807225 |
| [66] | Das, S., J. High Energy Phys., 1999, 06 (1999), arXiv:hep-th/9905037 |
| [67] | Gonzalez-Rey, F.; Kulik, B.; Park, I.; Roček, M., Nuclear Phys. B, 544, 1-2 (1999), arXiv:hep-th/9810152 |
| [68] | Tanabashi, M., Phys. Rev. D, 98, Article 030001 pp. (2018) |
| [69] | Alday, L.; Maldacena, J., J. High Energy Phys., 2007, 06, 064 (2007), arXiv:0705.0303 [hep-th] |
| [70] | Hartnoll, S.; Herzog, C.; Horowitz, G., Phys. Rev. Lett., 101, 3 (2008), arXiv:0803.3295 [hep-th] |
| [71] | Gubser, S., Phys. Rev. D, 78, 6 (2008), arXiv:0801.2977 [hep-th] |
| [72] | Maeda, K.; Natsuume, M.; Okamura, T., Phys. Rev. D, 79, 12 (2009), arXiv:0904.1914 [hep-th] |
| [73] | Hartnoll, S., Classical Quantum Gravity, 26, 22, Article 224002 pp. (2009), arXiv:0903.3246 [hep-th] · Zbl 1181.83003 |
| [74] | Einstein, A., Ann. Phys., 17, 549-560, 208 (1905) · JFM 36.0975.01 |
| [75] | Smoluchowski, M., Ann. Phys., 21, 756-780 (1906) · JFM 37.0814.03 |
| [76] | Brush, S., Arch. Hist. Exact Sci., 5, 1, 1-36 (1968) · Zbl 0177.29803 |
| [77] | Bachelier, L., Theory of Speculation (1900); Dimson, E.; Mussavian, M., Eur. Financ. Manag., 4, 1, 91-193 (1998) |
| [78] | Wiener, N., J. Math. Phys., 2, 1-4, 131-174 (1923) · JFM 49.0412.10 |
| [79] | Langevin, P., Amer. J. Phys., 65, 11, 1079-1081 (1997) |
| [80] | Uhlenbeck, G.; Ornstein, L., Phys. Rev., 36, 5, 823 (1930) · JFM 56.1277.03 |
| [81] | Pottier, N., Nonequilibrium Statistical Physics: Linear Irreversible Processes (2010), Oxford University Press · Zbl 1191.82001 |
| [82] | Kubo, R., Rep. Progr. Phys., 29, 1, 255 (1966) · Zbl 0163.23102 |
| [83] | Ornstein, L., Acad. Amst., 26, 1005 (1917) |
| [84] | Mori, H., Progr. Theoret. Phys., 33, 3, 423-455 (1965) · Zbl 0127.45002 |
| [85] | Wiener, N., Acta Math., 55, 117-258 (1930) · JFM 56.0954.02 |
| [86] | Wang, M.; Uhlenbeck, G., Rev. Modern Phys., 17, 2-3, 323 (1945) · Zbl 0063.08172 |
| [87] | Dunkel, J.; Hänggi, P., Phys. Rep., 471, 1, 1-73 (2009), arXiv:0812.1996 [hep-th] |
| [88] | Kubo, R.; Toda, M.; Hashitsume, N., Statistical Physics II: Nonequilibrium Statistical Mechanics, Vol. 31 (2012), Springer Science & Business Media |
| [89] | Brink, L.; Di Vecchia, P.; Howe, P., Phys. Lett. B, 65, 5, 471-474 (1976) |
| [90] | Deser, S.; Zumino, B., Phys. Lett. B, 65, 4, 369-373 (1976) |
| [91] | Polyakov, A., (Supergravities in Diverse Dimensions: Commentary and Reprints (in 2 Volumes) (1989), World Scientific), 1197-1200 |
| [92] | Zwiebach, B., A First Course in String Theory (2004), Cambridge University Press · Zbl 1072.81001 |
| [93] | Polchinski, J., String Theory: Volume 1, an Introduction to the Bosonic String (1998), Cambridge University Press · Zbl 1006.81521 |
| [94] | Nambu, Y., (Broken Symmetry: Selected Papers of Y Nambu (1995), World Scientific), 280-301 · Zbl 0898.01021 |
| [95] | Gotō, T., Progr. Theoret. Phys., 46, 5, 1560-1569 (1971) · Zbl 1098.81531 |
| [96] | Carroll, S., Spacetime and Geometry: An Introduction to General Relativity (2004), Addison Wesley · Zbl 1131.83001 |
| [97] | Wolfram Research Inc., Mathematica, version 11.3 (2018), Champaign, IL |
| [98] | Rich, A.; Scheibe, P.; Abbasi, N., J. Open Source Softw., 3, 32, 1073 (2018) |
| [99] | Bañados, M.; Teitelboim, C.; Zanelli, J., Phys. Rev. Lett., 69, 13, 1849-1851 (1992), arXiv:hep-th/9204099 · Zbl 0968.83514 |
| [100] | Bardeen, W.; Bars, I.; Hanson, A.; Peccei, R., Phys. Rev. D, 13, 8, 2364 (1976) |
| [101] | Gubser, S.; Gulotta, D.; Pufu, S.; Rocha, F., J. High Energy Phys., 2008, 10, 052 (2008), arXiv:0803.1470 [hep-th] · Zbl 1245.81242 |
| [102] | Chesler, P.; Jensen, K.; Karch, A., Phys. Rev. D, 79, 2 (2009), arXiv:0804.3110 [hep-th] |
| [103] | Chesler, P.; Jensen, K.; Karch, A.; Yaffe, L., Phys. Rev. D, 79, 12 (2009), arXiv:0810.1985 [hep-th] |
| [104] | Ficnar, A., Phys. Rev. D, 86, 4 (2012), arXiv:1201.1780 [hep-th] |
| [105] | Ficnar, A.; Noronha, J.; Gyulassy, M., Nuclear Phys. A, 910-911, 252-255 (2013), arXiv:1208.0305 [hep-th] |
| [106] | Ficnar, A.; Gubser, S., Phys. Rev. D, 89, 2 (2014), arXiv:1306.6648 [hep-th] |
| [107] | Bars, I., (Second Paris Cosmology Colloquium (1994), World Scientific), 399, arXiv:hep-th/9411217 |
| [108] | Bars, I.; Schulze, J., Phys. Rev. D, 51, 4, 1854-1868 (1995), arXiv:hep-th/9405156 |
| [109] | Álvarez, E.; Conde, J., Modern Phys. Lett. A, 17, 07, 413-420 (2002), arXiv:gr-qc/0111031 · Zbl 1083.81566 |
| [110] | Matsuo, T.; Tomino, D.; Wen, W., J. High Energy Phys., 2006, 10 (2006), arXiv:hep-th/0607178 |
| [111] | Kim, K.; Shock, J.; Tarrío, J., J. High Energy Phys., 2011, 6 (2011), arXiv:1103.4581 [hep-th] |
| [112] | Cederwall, M.; von Gussich, A.; Mikovic, A.; Nilsson, B.; Westerberg, A., Phys. Lett. B, 390, 1-4 (1997), arXiv:hep-th/9606173 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
