Advertisement

Hydrodynamics from scalar black branes

  • Dibakar Roychowdhury
Open Access
Regular Article - Theoretical Physics

Abstract

In this paper, using the Gauge/gravity duality techniques, we explore the hydrodynamic regime of a very special class of strongly coupled QFTs that come up with an emerging UV length scale in the presence of a negative hyperscaling violating exponent. The dual gravitational counterpart for these QFTs consists of scalar dressed black brane solutions of exactly integrable Einstein-scalar gravity model with Domain Wall (DW) asymptotics. In the first part of our analysis we compute the R-charge diffusion for the boundary theory and find that (unlike the case for the pure AdS4 black branes) it scales quite non trivially with the temperature. In the second part of our analysis, we compute the η/s ratio both in the non extremal as well as in the extremal limit of these special class of gauge theories and it turns out to be equal to 1/4π in both the cases. These results therefore suggest that the quantum critical systems in the presence of (negative) hyperscaling violation at UV, might fall under a separate universality class as compared to those conventional quantum critical systems with the usual AdS4 duals.

Keywords

Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) Black Holes 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  2. [2]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    J.-P. Wu and H.-B. Zeng, Dynamic gap from holographic fermions in charged dilaton black branes, JHEP 04 (2012) 068 [arXiv:1201.2485] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    C. Charmousis, B. Gouteraux and J. Soda, Einstein-Maxwell-dilaton theories with a Liouville potential, Phys. Rev. D 80 (2009) 024028 [arXiv:0905.3337] [INSPIRE].ADSMathSciNetGoogle Scholar
  5. [5]
    K. Goldstein, S. Kachru, S. Prakash and S.P. Trivedi, Holography of charged dilaton black holes, JHEP 08 (2010) 078 [arXiv:0911.3586] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP 12 (2011) 036 [arXiv:1107.2116] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  7. [7]
    M. Cadoni, G. D’Appollonio and P. Pani, Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime, JHEP 03 (2010) 100 [arXiv:0912.3520] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    K. Goldstein et al., Holography of dyonic dilaton black branes, JHEP 10 (2010) 027 [arXiv:1007.2490] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  9. [9]
    S. Jain, N. Kundu, K. Sen, A. Sinha and S.P. Trivedi, A strongly coupled anisotropic fluid from dilaton driven holography, JHEP 01 (2015) 005 [arXiv:1406.4874] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Cadoni and P. Pani, Holography of charged dilatonic black branes at finite temperature, JHEP 04 (2011) 049 [arXiv:1102.3820] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    B.-H. Lee, D.-W. Pang and C. Park, A holographic model of strange metals, Int. J. Mod. Phys. A 26 (2011) 2279 [arXiv:1107.5822] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    G. Bertoldi, B.A. Burrington and A.W. Peet, Thermal behavior of charged dilatonic black branes in AdS and UV completions of Lifshitz-like geometries, Phys. Rev. D 82 (2010) 106013 [arXiv:1007.1464] [INSPIRE].ADSGoogle Scholar
  13. [13]
    J.R. David, M. Mahato and S.R. Wadia, Hydrodynamics from the D1-brane, JHEP 04 (2009) 042 [arXiv:0901.2013] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    J.R. David, M. Mahato, S. Thakur and S.R. Wadia, Hydrodynamics of R-charged D1-branes, JHEP 01 (2011) 014 [arXiv:1008.4350] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity, JHEP 01 (2012) 094 [arXiv:1105.1162] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  16. [16]
    M. Cadoni, S. Mignemi and M. Serra, Exact solutions with AdS asymptotics of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field, Phys. Rev. D 84 (2011) 084046 [arXiv:1107.5979] [INSPIRE].ADSGoogle Scholar
  17. [17]
    G. Bertoldi, B.A. Burrington, A.W. Peet and I.G. Zadeh, Lifshitz-like black brane thermodynamics in higher dimensions, Phys. Rev. D 83 (2011) 126006 [arXiv:1101.1980] [INSPIRE].ADSGoogle Scholar
  18. [18]
    X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, Aspects of holography for theories with hyperscaling violation, JHEP 06 (2012) 041 [arXiv:1201.1905] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    J. Sadeghi, B. Pourhasan and F. Pourasadollah, Thermodynamics of Schrödinger black holes with hyperscaling violation, Phys. Lett. B 720 (2013) 244 [arXiv:1209.1874] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  20. [20]
    B.S. Kim, Schrödinger holography with and without hyperscaling violation, JHEP 06 (2012) 116 [arXiv:1202.6062] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S.A. Hartnoll and E. Shaghoulian, Spectral weight in holographic scaling geometries, JHEP 07 (2012) 078 [arXiv:1203.4236] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    M. Alishahiha, E. O Colgain and H. Yavartanoo, Charged black branes with hyperscaling violating factor, JHEP 11 (2012) 137 [arXiv:1209.3946] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Alishahiha and H. Yavartanoo, On holography with hyperscaling violation, JHEP 11 (2012) 034 [arXiv:1208.6197] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J. Bhattacharya, S. Cremonini and A. Sinkovics, On the IR completion of geometries with hyperscaling violation, JHEP 02 (2013) 147 [arXiv:1208.1752] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    L. Huijse, S. Sachdev and B. Swingle, Hidden Fermi surfaces in compressible states of gauge-gravity duality, Phys. Rev. B 85 (2012) 035121 [arXiv:1112.0573] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    W.-J. Li and J.-P. Wu, Holographic fermions in charged dilaton black branes, Nucl. Phys. B 867 (2013) 810 [arXiv:1203.0674] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    E. Shaghoulian, Holographic entanglement entropy and Fermi surfaces, JHEP 05 (2012) 065 [arXiv:1112.2702] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  28. [28]
    N. Ogawa, T. Takayanagi and T. Ugajin, Holographic Fermi surfaces and entanglement entropy, JHEP 01 (2012) 125 [arXiv:1111.1023] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    M. Kulaxizi, A. Parnachev and K. Schalm, On holographic entanglement entropy of charged matter, JHEP 10 (2012) 098 [arXiv:1208.2937] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    M. Cadoni, S. Mignemi and M. Serra, Black brane solutions and their solitonic extremal limit in Einstein-scalar gravity, Phys. Rev. D 85 (2012) 086001 [arXiv:1111.6581] [INSPIRE].ADSGoogle Scholar
  31. [31]
    M. Cadoni and S. Mignemi, Phase transition and hyperscaling violation for scalar Black Branes, JHEP 06 (2012) 056 [arXiv:1205.0412] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    M. Cadoni and M. Serra, Hyperscaling violation for scalar black branes in arbitrary dimensions, JHEP 11 (2012) 136 [arXiv:1209.4484] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    D.S. Fisher, Scaling and critical slowing down in random-field Ising systems, Phys. Rev. Lett. 56 (1986) 416 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    P. Kovtun and A. Ritz, Universal conductivity and central charges, Phys. Rev. D 78 (2008) 066009 [arXiv:0806.0110] [INSPIRE].ADSGoogle Scholar
  36. [36]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    G. Policastro, D.T. Son and A.O. Starinets, The shear viscosity of strongly coupled N = 4 supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 87 (2001) 081601 [hep-th/0104066] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    R. Brustein and A.J.M. Medved, The ratio of shear viscosity to entropy density in generalized theories of gravity, Phys. Rev. D 79 (2009) 021901 [arXiv:0808.3498] [INSPIRE].ADSGoogle Scholar
  40. [40]
    A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    O. Saremi, The viscosity bound conjecture and hydrodynamics of M2-brane theory at finite chemical potential, JHEP 10 (2006) 083 [hep-th/0601159] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    D.T. Son and A.O. Starinets, Hydrodynamics of r-charged black holes, JHEP 03 (2006) 052 [hep-th/0601157] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  43. [43]
    A. Buchel, J.T. Liu and A.O. Starinets, Coupling constant dependence of the shear viscosity in N = 4 supersymmetric Yang-Mills theory, Nucl. Phys. B 707 (2005) 56 [hep-th/0406264] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    A. Buchel, Shear viscosity of CFT plasma at finite coupling, Phys. Lett. B 665 (2008) 298 [arXiv:0804.3161] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  45. [45]
    P. Benincasa and A. Buchel, Transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling, JHEP 01 (2006) 103 [hep-th/0510041] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    J. Mas, Shear viscosity from R-charged AdS black holes, JHEP 03 (2006) 016 [hep-th/0601144] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [INSPIRE].ADSGoogle Scholar
  48. [48]
    M. Edalati, J.I. Jottar and R.G. Leigh, Transport Coefficients at Zero Temperature from Extremal Black Holes, JHEP 01 (2010) 018 [arXiv:0910.0645] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  49. [49]
    S.K. Chakrabarti, S. Jain and S. Mukherji, Viscosity to entropy ratio at extremality, JHEP 01 (2010) 068 [arXiv:0910.5132] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  50. [50]
    M. Edalati, J.I. Jottar and R.G. Leigh, Shear modes, criticality and extremal black holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  51. [51]
    M.F. Paulos, Transport coefficients, membrane couplings and universality at extremality, JHEP 02 (2010) 067 [arXiv:0910.4602] [INSPIRE].ADSCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia

Personalised recommendations