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Charged, conformal non-relativistic hydrodynamics

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Abstract

We embed a holographic model of an U(1) charged fluid with Galilean invariance in string theory and calculate its specific heat capacity and Prandtl number. Such theories are generated by a R-symmetry twist along a null direction of a \( \mathcal{N} = 1 \) superconformal theory. We study the hydrodynamic properties of such systems employing ideas from the fluid-gravity correspondence.

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References

  1. PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/0410003] [SPIRES].

    ADS  Google Scholar 

  2. B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757 (2005) 28 [nucl-ex/0410022] [SPIRES].

    ADS  Google Scholar 

  3. BRAHMS collaboration, I. Arsene et al., Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys. A 757 (2005) 1 [nucl-ex/0410020] [SPIRES].

    ADS  Google Scholar 

  4. T. Schafer and D. Teaney, Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas, Rept. Prog. Phys. 72 (2009) 126001 [arXiv:0904.3107] [SPIRES].

    Article  ADS  Google Scholar 

  5. H. Nastase, The RHIC fireball as a dual black hole, hep-th/0501068 [SPIRES].

  6. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].

    MATH  MathSciNet  ADS  Google Scholar 

  7. S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  8. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  9. M. Rangamani, Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics. II: Sound waves, JHEP 12 (2002) 054 [hep-th/0210220] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  12. S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [SPIRES].

    Article  ADS  Google Scholar 

  13. C.R. Hagen, Scale and conformal transformations in galilean-covariant field theory, Phys. Rev. D5 (1972) 377 [SPIRES].

    ADS  Google Scholar 

  14. T. Mehen, I.W. Stewart and M.B. Wise, Conformal invariance for non-relativistic field theory, Phys. Lett. B 474 (2000) 145 [hep-th/9910025] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  15. Y. Nishida and D.T. Son, Nonrelativistic conformal field theories, Phys. Rev. D 76 (2007) 086004 [arXiv:0706.3746] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  16. D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  17. K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. C.P. Herzog, M. Rangamani and S.F. Ross, Heating up Galilean holography, JHEP 11 (2008) 080 [arXiv:0807.1099] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. J. Maldacena, D. Martelli and Y. Tachikawa, Comments on string theory backgrounds with non-relativistic conformal symmetry, JHEP 10 (2008) 072 [arXiv:0807.1100] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. A. Adams, K. Balasubramanian and J. McGreevy, Hot Spacetimes for Cold Atoms, JHEP 11 (2008) 059 [arXiv:0807.1111] [SPIRES].

    Article  ADS  Google Scholar 

  21. S.F. Ross and O. Saremi, Holographic stress tensor for non-relativistic theories, JHEP 09 (2009) 009 [arXiv:0907.1846] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. W.D. Goldberger, AdS/CFT duality for non-relativistic field theory, JHEP 03 (2009) 069 [arXiv:0806.2867] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. J.L.F. Barbon and C.A. Fuertes, On the spectrum of nonrelativistic AdS/CFT, JHEP 09 (2008) 030 [arXiv:0806.3244] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. W.-Y. Wen, AdS/NRCFT for the(super) Calogero model, arXiv:0807.0633 [SPIRES].

  25. Y. Nakayama, Index for Non-relativistic Superconformal Field Theories, JHEP 10 (2008) 083 [arXiv:0807.3344] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  26. J.-W. Chen and W.-Y. Wen, Shear Viscosity of a Non-Relativistic Conformal Gas in Two Dimensions, arXiv:0808.0399 [SPIRES].

  27. D. Minic and M. Pleimling, Non-relativistic AdS/CFT and Aging/Gravity Duality, Phys. Rev. E 78 (2008) 061108 [arXiv:0807.3665] [SPIRES].

    ADS  Google Scholar 

  28. E. Imeroni, On deformed gauge theories and their string/M-theory duals, JHEP 10 (2008) 026 [arXiv:0808.1271] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. A.V. Galajinsky, Remark on quantum mechanics with conformal Galilean symmetry, Phys. Rev. D 78 (2008) 087701 [arXiv:0808.1553] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  30. S. Kachru, X. Liu and M. Mulligan, Gravity Duals of Lifshitz-like Fixed Points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  31. S.S. Pal, Null Melvin Twist to Sakai-Sugimoto model, arXiv:0808.3042 [SPIRES].

  32. S. Sekhar Pal, Towards Gravity solutions of AdS/CMT, arXiv:0808.3232 [SPIRES].

  33. S. Pal, More gravity solutions of AdS/CMT, arXiv:0809.1756 [SPIRES].

  34. P. Kovtun and D. Nickel, Black holes and non-relativistic quantum systems, Phys. Rev. Lett. 102 (2009) 011602 [arXiv:0809.2020] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. C. Duval, M. Hassaine and P.A. Horvathy, The geometry of Schródinger symmetry in gravity background/non-relativistic CFT, Annals Phys. 324 (2009) 1158 [arXiv:0809.3128] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  36. D. Yamada, Thermodynamics of Black Holes in Schroedinger Space, Class. Quant. Grav. 26 (2009) 075006 [arXiv:0809.4928] [SPIRES].

    Article  ADS  Google Scholar 

  37. F.-L. Lin and S.-Y. Wu, Non-relativistic Holography and Singular Black Hole, Phys. Lett. B 679 (2009) 65 [arXiv:0810.0227] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  38. S.A. Hartnoll and K. Yoshida, Families of IIB duals for nonrelativistic CFTs, JHEP 12 (2008) 071 [arXiv:0810.0298] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. M. Schvellinger, Kerr-AdS black holes and non-relativistic conformal QM theories in diverse dimensions, JHEP 12 (2008) 004 [arXiv:0810.3011] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  40. L. Mazzucato, Y. Oz and S. Theisen, Non-relativistic Branes, JHEP 04 (2009) 073 [arXiv:0810.3673] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. C. Leiva and M.S. Plyushchay, Conformal symmetry of relativistic and nonrelativistic systems and AdS/CFT correspondence, Ann. Phys. 307 (2003) 372 [hep-th/0301244] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  42. M. Hassaïne and P.A. Horváthy, Field-dependent symmetries of a non-relativistic fluid model, Ann. Phys. 282 (2000) 218 [math-ph/9904022] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  43. M. Hassaïne and P.A. Horváthy, Symmetries of fluid dynamics with polytropic exponent, Phys. Lett. A 279 (2001) 215 [hep-th/0009092] [SPIRES].

    ADS  Google Scholar 

  44. P.A. Horváthy and P.M. Zhang, Non-relativistic conformal symmetries in fluid mechanics, Eur. Phys. J. C 65 (2010) 607 [arXiv:0906.3594] [SPIRES].

    Google Scholar 

  45. A. Ghodsi and M. Alishahiha, Non-relativistic D3-brane in the presence of higher derivative corrections, Phys. Rev. D 80 (2009) 026004 [arXiv:0901.3431] [SPIRES].

    ADS  Google Scholar 

  46. J.P. Gauntlett, S. Kim, O. Varela and D. Waldram, Consistent supersymmetric Kaluza–Klein truncations with massive modes, JHEP 04 (2009) 102 [arXiv:0901.0676] [SPIRES].

    Article  ADS  Google Scholar 

  47. A. Donos and J.P. Gauntlett, Supersymmetric solutions for non-relativistic holography, JHEP 03 (2009) 138 [arXiv:0901.0818] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  48. A. Donos and J.P. Gauntlett, Solutions of type IIB and D = 11 supergravity with Schrödinger(z) symmetry, JHEP 07 (2009) 042 [arXiv:0905.1098] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  49. A. Donos and J.P. Gauntlett, Schrödinger invariant solutions of type IIB with enhanced supersymmetry, JHEP 10 (2009) 073 [arXiv:0907.1761] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. M. Rangamani, S.F. Ross, D.T. Son and E.G. Thompson, Conformal non-relativistic hydrodynamics from gravity, JHEP 01 (2009) 075 [arXiv:0811.2049] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. D.T. Son and P. Surowka, Hydrodynamics with Triangle Anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  52. A. Adams, C.M. Brown, O. DeWolfe and C. Rosen, Charged Schrödinger Black Holes, Phys. Rev. D 80 (2009) 125018 [arXiv:0907.1920] [SPIRES].

    ADS  Google Scholar 

  53. E. Imeroni and A. Sinha, Non-relativistic metrics with extremal limits, JHEP 09 (2009) 096 [arXiv:0907.1892] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. R.R. Nayak, K.L. Panigrahi and S. Siwach, Brane solutions with/ without rotationin pp-wave spacetime, Nucl. Phys. B 698 (2004) 149 [hep-th/0405124] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  55. M. Alishahiha and O.J. Ganor, Twisted backgrounds, pp-waves and nonlocal field theories, JHEP 03 (2003) 006 [hep-th/0301080] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  56. E.G. Gimon, A. Hashimoto, V.E. Hubeny, O. Lunin and M. Rangamani, Black strings in asymptotically plane wave geometries, JHEP 08 (2003)035 [hep-th/0306131] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  57. O. Lunin and J.M. Maldacena, Deforming field theories with U(1) × U(1) global symmetry and their gravity duals, JHEP 05 (2005) 033 [hep-th/0502086] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  58. S. Bhattacharyya, S. Minwalla and S.R. Wadia, The Incompressible Non-Relativistic Navier-Stokes Equation from Gravity, JHEP 08 (2009) 059 [arXiv:0810.1545] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  59. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics. Vol.6: Fluid Mechanics, second edition, Butterworth-Heinemann, Oxford U.K.(1987).

  60. W. Israel, Nonstationary irreversible thermodynamics: A Causal relativistic theory, Ann. Phys. 100 (1976) 310 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  61. W. Israel and J.M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. 118 (1979) 341 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  62. V. Balasubramanian and P. Kraus, A stress tensor for anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  63. A. Buchel and J.T. Liu, Gauged supergravity from type IIB string theory on Y(p,q) manifolds, Nucl. Phys. B 771 (2007) 93 [hep-th/0608002] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  64. N. Banerjee et al., Hydrodynamics from charged black branes, arXiv:0809.2596 [SPIRES].

  65. J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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  1. Centre for Particle Theory & Department of Mathematical Sciences, Science Laboratories, South Road, Durham, DH1 3LE, U.K.

    Daniel K. Brattan

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Brattan, D.K. Charged, conformal non-relativistic hydrodynamics. J. High Energ. Phys. 2010, 15 (2010). https://doi.org/10.1007/JHEP10(2010)015

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