Abstract
We study the velocity statistics distribution of an external heavy particle in holographic fluids. We argue that when the dual supergravity background has a finite temperature horizon the velocity statistics goes generically as 1/v, compatible with the jet-quenching intuition from the quark-gluon plasma. A careful analysis of the behavior of the classical string whose apparent world sheet horizon deviates from the background horizon reveals that other regimes are possible. We numerically discuss two cases: the magnetized quark-gluon plasma and a model of superfluid flow. We explore a range of parameters in these top-down supergravity solutions including, respectively, the magnetic field and the superfluid velocity. We determine that the velocity statistics goes largely as 1/v, however, as we leave the non-relativistic regime we observe some deviations.
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D.T. Son and A.O. Starinets, Viscosity, black holes and quantum field theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [INSPIRE].
M. Rangamani, Gravity and hydrodynamics: lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
M. Chernicoff and A. Guijosa, Acceleration, energy loss and screening in strongly-coupled gauge theories, JHEP 06 (2008) 005 [arXiv:0803.3070] [INSPIRE].
E. Caceres and A. Guijosa, On drag forces and jet quenching in strongly coupled plasmas, JHEP 12 (2006) 068 [hep-th/0606134] [INSPIRE].
M. Mahato, L.A. Pando Zayas and C.A. Terrero-Escalante, Black holes in cascading theories: confinement/deconfinement transition and other thermal properties, JHEP 09 (2007) 083 [arXiv:0707.2737] [INSPIRE].
M.S. Paoletti, M.E. Fisher, K.R. Sreenivasan and D.P. Lathrop, Velocity statistics distinguish quantum turbulence from classical turbulence, Phys. Rev. Lett. 101 (2008) 154501.
C.F. Barenghi, L. Skrbek and K.R. Sreenivasan, Introduction to quantum turbulence, Proc. Nat. Acad. Sci. 111 (2014) 4647.
S.S. Gubser and A. Yarom, Pointlike probes of superstring-theoretic superfluids, JHEP 03 (2010) 041 [arXiv:0908.1392] [INSPIRE].
A. Adams, P.M. Chesler and H. Liu, Holographic turbulence, Phys. Rev. Lett. 112 (2014) 151602 [arXiv:1307.7267] [INSPIRE].
S.R. Green, F. Carrasco and L. Lehner, Holographic path to the turbulent side of gravity, Phys. Rev. X 4 (2014) 011001 [arXiv:1309.7940] [INSPIRE].
A. Adams, P.M. Chesler and H. Liu, Holographic vortex liquids and superfluid turbulence, Science 341 (2013) 368 [arXiv:1212.0281] [INSPIRE].
C. Ewerz, T. Gasenzer, M. Karl and A. Samberg, Non-thermal fixed point in a holographic superfluid, JHEP 05 (2015) 070 [arXiv:1410.3472] [INSPIRE].
Y. Du, C. Niu, Y. Tian and H. Zhang, Holographic thermal relaxation in superfluid turbulence, JHEP 12 (2015) 018 [arXiv:1412.8417] [INSPIRE].
S. Lan, Y. Tian and H. Zhang, Towards quantum turbulence in finite temperature Bose-Einstein condensates, JHEP 07 (2016) 092 [arXiv:1605.01193] [INSPIRE].
S.I. Finazzo, R. Critelli, R. Rougemont and J. Noronha, Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields, Phys. Rev. D 94 (2016) 054020 [arXiv:1605.06061] [INSPIRE].
N. Drukker and B. Fiol, All-genus calculation of Wilson loops using D-branes, JHEP 02 (2005) 010 [hep-th/0501109] [INSPIRE].
J. Gomis and F. Passerini, Holographic Wilson loops, JHEP 08 (2006) 074 [hep-th/0604007] [INSPIRE].
C.P. Herzog and I.R. Klebanov, On string tensions in supersymmetric SU(M ) gauge theory, Phys. Lett. B 526 (2002) 388 [hep-th/0111078] [INSPIRE].
E. D’Hoker and P. Kraus, Magnetic brane solutions in AdS, JHEP 10 (2009) 088 [arXiv:0908.3875] [INSPIRE].
D. Arean, M. Bertolini, C. Krishnan and T. Prochazka, Type IIB holographic superfluid flows, JHEP 03 (2011) 008 [arXiv:1010.5777] [INSPIRE].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].
E. Shuryak, Why does the quark gluon plasma at RHIC behave as a nearly ideal fluid?, Prog. Part. Nucl. Phys. 53 (2004) 273 [hep-ph/0312227] [INSPIRE].
E.V. Shuryak, What RHIC experiments and theory tell us about properties of quark-gluon plasma?, Nucl. Phys. A 750 (2005) 64 [hep-ph/0405066] [INSPIRE].
J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].
G. Basar, D. Kharzeev, D. Kharzeev and V. Skokov, Conformal anomaly as a source of soft photons in heavy ion collisions, Phys. Rev. Lett. 109 (2012) 202303 [arXiv:1206.1334] [INSPIRE].
ALICE collaboration, M. Wilde, Measurement of direct photons in pp and Pb-Pb collisions with ALICE, Nucl. Phys. A904-905 (2013) 573c-576c [arXiv:1210.5958] [INSPIRE].
PHENIX collaboration, A. Adare et al., Observation of direct-photon collective flow in \( \sqrt{s_{\mathrm{NN}}}=200 \) GeV Au + Au collisions, Phys. Rev. Lett. 109 (2012) 122302 [arXiv:1105.4126] [INSPIRE].
G. Arciniega, P. Ortega and L. Patiño, Brighter branes, enhancement of photon production by strong magnetic fields in the gauge/gravity correspondence, JHEP 04 (2014) 192 [arXiv:1307.1153] [INSPIRE].
A. Nata Atmaja and K. Schalm, Anisotropic drag force from 4D Kerr-AdS black holes, JHEP 04 (2011) 070 [arXiv:1012.3800] [INSPIRE].
M. Chernicoff, D. Fernandez, D. Mateos and D. Trancanelli, Drag force in a strongly coupled anisotropic plasma, JHEP 08 (2012) 100 [arXiv:1202.3696] [INSPIRE].
D. Giataganas, Probing strongly coupled anisotropic plasma, JHEP 07 (2012) 031 [arXiv:1202.4436] [INSPIRE].
A.V. Sadofyev and Y. Yin, Drag suppression in anomalous chiral media, Phys. Rev. D 93 (2016) 125026 [arXiv:1511.08794] [INSPIRE].
U. Elinos and L. Patiño, Holographic implications of a magnetic brane lift to ten dimensions, to appear.
T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
E. D’Hoker, P. Kraus and A. Shah, RG flow of magnetic brane correlators, JHEP 04 (2011) 039 [arXiv:1012.5072] [INSPIRE].
E. D’Hoker and B. Pourhamzeh, Emergent super-Virasoro on magnetic branes, JHEP 06 (2016) 146 [arXiv:1602.01487] [INSPIRE].
G.T. Horowitz, Introduction to holographic superconductors, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: vector hair for an AdS black hole, Phys. Rev. D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
J. Sonner and B. Withers, A gravity derivation of the Tisza-Landau model in AdS/CFT, Phys. Rev. D 82 (2010) 026001 [arXiv:1004.2707] [INSPIRE].
S.S. Gubser, S.S. Pufu and F.D. Rocha, Quantum critical superconductors in string theory and M-theory, Phys. Lett. B 683 (2010) 201 [arXiv:0908.0011] [INSPIRE].
D. Arean, M. Bertolini, C. Krishnan and T. Prochazka, Quantum critical superfluid flows and anisotropic domain walls, JHEP 09 (2011) 131 [arXiv:1106.1053] [INSPIRE].
S. Li, K.A. Mamo and H.-U. Yee, Jet quenching parameter of quark-gluon plasma in strong magnetic field: perturbative QCD and AdS/CFT correspondence, arXiv:1605.00188 [INSPIRE].
K.A. Mamo, Energy loss of a nonaccelerating quark moving through a strongly coupled N = 4 super Yang-Mills vacuum or plasma in strong magnetic field, Phys. Rev. D 94 (2016) 041901 [arXiv:1606.01598] [INSPIRE].
G.V. Kolmakov, P.V.E. McClintock and S.V. Nazarenko, Wave turbulence in quantum fluids, Proc. Nat. Acad. Sci. 111 (2014) 4727.
P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
H.P. de Oliveira, L.A. Pando Zayas and E.L. Rodrigues, A Kolmogorov-Zakharov spectrum in AdS gravitational collapse, Phys. Rev. Lett. 111 (2013) 051101 [arXiv:1209.2369] [INSPIRE].
V.S. L’vov, S.V. Nazarenko and O. Rudenko, Bottleneck crossover between classical and quantum superfluid turbulence, Phys. Rev. B 76 (2007) 024520.
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Areán, D., Zayas, L.A.P., Patiño, L. et al. Velocity statistics in holographic fluids: magnetized quark-gluon plasma and superfluid flow. J. High Energ. Phys. 2016, 158 (2016). https://doi.org/10.1007/JHEP10(2016)158
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DOI: https://doi.org/10.1007/JHEP10(2016)158