Spectral functions in V-QCD with matter: masses, susceptibilities, diffusion and conductivity

Open Access
Regular Article - Theoretical Physics

Abstract

We consider a holographic model of QCD in the Veneziano limit of a large number of colors N c and flavors N f but fixed x = N f /N c (V-QCD). The model exhibits a first order deconfined but chirally broken transition, followed by a second order chirally restored transition in the μT plane for a range of plausible holographic parameters. We study the quasi-normal mode spectrum, and derive the pertinent vector and axial spectral functions across the transition regions. The pole masses, susceptibilities, diffusion constants and electric conductivity are also discussed. In particular, the pole masses are found to survive the deconfining transition, to quickly dissolve in the the chirally restored phase by developing substantial widths. The flavor electric conductivities arise sharply in the transition region. The flavor susceptibility is shown to be consistent with the one derived from bulk thermodynamics.

Keywords

Quark-Gluon Plasma Gauge-gravity correspondence Holography and quarkgluon plasmas Phase Diagram of QCD 

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]
    I.M. Barbour, S.E. Morrison, E.G. Klepfish, J.B. Kogut and M.-P. Lombardo, Results on finite density QCD, Nucl. Phys. Proc. Suppl. 60A (1998) 220 [hep-lat/9705042] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The QCD phase diagram at nonzero quark density, JHEP 04 (2011) 001 [arXiv:1102.1356] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    C.W. Bernard et al., The spatial structure of screening propagators in hot QCD, Phys. Rev. Lett. 68 (1992) 2125 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    P. Petreczky, Lattice calculations of meson correlators and spectral functions at finite temperature, J. Phys. G 30 (2004) S431 [hep-ph/0305189] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    P. Petreczky, Lattice QCD at non-zero temperature, J. Phys. G 39 (2012) 093002 [arXiv:1203.5320] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    T.H. Hansson and I. Zahed, Hadronic correlators in hot QCD, Nucl. Phys. B 374 (1992) 277 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    A. Fayyazuddin, T.H. Hansson, M.A. Nowak, J.J.M. Verbaarschot and I. Zahed, Finite temperature correlators in the Schwinger model, Nucl. Phys. B 425 (1994) 553 [hep-ph/9312362] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    T.H. Hansson, M. Sporre and I. Zahed, Baryonic and gluonic correlators in hot QCD, Nucl. Phys. B 427 (1994) 545 [hep-ph/9401281] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T.H. Hansson, J. Wirstam and I. Zahed, Real time correlators in hot (2 + 1)-dimensions QCD, Phys. Rev. D 58 (1998) 065012 [hep-th/9705026] [INSPIRE].ADSGoogle Scholar
  10. [10]
    D. Sexty, Progress in complex Langevin simulations of full QCD at non-zero density, Nucl. Phys. A 931 (2014) 856 [arXiv:1408.6767] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Sch1458äfer and E.V. Shuryak, Instantons in QCD, Rev. Mod. Phys. 70 (1998) 323 [hep-ph/9610451] [INSPIRE].
  12. [12]
    D. Diakonov, Instantons at work, Prog. Part. Nucl. Phys. 51 (2003) 173 [hep-ph/0212026] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    M.A. Nowak, M. Rho and I. Zahed, Chiral nuclear dynamics, World Scientific, Singapore (1996).CrossRefGoogle Scholar
  14. [14]
    C. Ratti, S. Roessner, M.A. Thaler and W. Weise, Thermodynamics of the PNJL model, Eur. Phys. J. C 49 (2007) 213 [hep-ph/0609218] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    C. Ratti, S. Roessner and W. Weise, Quark number susceptibilities: Lattice QCD versus PNJL model, Phys. Lett. B 649 (2007) 57 [hep-ph/0701091] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    D. Diakonov, Statistical physics of dyons and confinement, Acta Phys. Polon. B 39 (2008) 3365 [arXiv:0807.0902] [INSPIRE].ADSGoogle Scholar
  17. [17]
    J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  18. [18]
    J. Babington, J. Erdmenger, N.J. Evans, Z. Guralnik and I. Kirsch, Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals, Phys. Rev. D 69 (2004) 066007 [hep-th/0306018] [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  19. [19]
    N.J. Evans and J.P. Shock, Chiral dynamics from AdS space, Phys. Rev. D 70 (2004) 046002 [hep-th/0403279] [INSPIRE].ADSMathSciNetGoogle Scholar
  20. [20]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  22. [22]
    J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    L. Da Rold and A. Pomarol, Chiral symmetry breaking from five dimensional spaces, Nucl. Phys. B 721 (2005) 79 [hep-ph/0501218] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  24. [24]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [INSPIRE].CrossRefGoogle Scholar
  25. [25]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    E. Kiritsis, Dissecting the string theory dual of QCD, Fortsch. Phys. 57 (2009) 396 [arXiv:0901.1772] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved holographic QCD, Lect. Notes Phys. 828 (2011) 79 [arXiv:1006.5461] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  28. [28]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and gluon plasma dynamics in improved holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  30. [30]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Improved holographic Yang-Mills at finite temperature: comparison with data, Nucl. Phys. B 820 (2009) 148 [arXiv:0903.2859] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  31. [31]
    A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    F. Bigazzi, R. Casero, A.L. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFTs with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    R. Casero, E. Kiritsis and A. Paredes, Chiral symmetry breaking as open string tachyon condensation, Nucl. Phys. B 787 (2007) 98 [hep-th/0702155] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from Sens tachyon action, Phys. Rev. D 81 (2010) 115004 [arXiv:1003.2377] [INSPIRE].ADSMATHGoogle Scholar
  35. [35]
    I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from tachyon condensation: II, JHEP 11 (2010) 123 [arXiv:1010.1364] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    G. Veneziano, Some aspects of a unified approach to gauge, dual and Gribov theories, Nucl. Phys. B 117 (1976) 519.ADSCrossRefGoogle Scholar
  37. [37]
    G. Veneziano, U(1) without instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    M. Järvinen and E. Kiritsis, Holographic models for QCD in the Veneziano limit, JHEP 03 (2012) 002 [arXiv:1112.1261] [INSPIRE].CrossRefMATHGoogle Scholar
  39. [39]
    T. Banks and A. Zaks, On the phase structure of vector-like gauge theories with massless fermions, Nucl. Phys. B 196 (1982) 189 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    B.A. Burrington, V.S. Kaplunovsky and J. Sonnenschein, Localized backreacted flavor branes in holographic QCD, JHEP 02 (2008) 001 [arXiv:0708.1234] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    F. Bigazzi and A.L. Cotrone, Holographic QCD with dynamical flavors, JHEP 01 (2015) 104 [arXiv:1410.2443] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis and K. Tuominen, On finite-temperature holographic QCD in the Veneziano limit, JHEP 01 (2013) 093 [arXiv:1210.4516] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    T. Alho et al., A holographic model for QCD in the Veneziano limit at finite temperature and density, JHEP 04 (2014) 124 [Erratum ibid. 1502 (2015) 033] [arXiv:1312.5199] [INSPIRE].
  44. [44]
    A. Stoffers and I. Zahed, Improved AdS/QCD model with matter, Phys. Rev. D 83 (2011) 055016 [arXiv:1009.4428] [INSPIRE].ADSGoogle Scholar
  45. [45]
    D. Arean, I. Iatrakis, M. Järvinen and E. Kiritsis, V-QCD: spectra, the dilaton and the S-parameter, Phys. Lett. B 720 (2013) 219 [arXiv:1211.6125] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    D. Arean, I. Iatrakis and M. Järvinen, The spectrum of (h)QCD in the Veneziano limit, PoS(Corfu2012)129 [arXiv:1305.6294] [INSPIRE].
  47. [47]
    D. Areán, I. Iatrakis, M. Järvinen and E. Kiritsis, The discontinuities of conformal transitions and mass spectra of V-QCD, JHEP 11 (2013) 068 [arXiv:1309.2286] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    T. Alho, Numerical code for thermodynamics of holographic V-QCD, https://github.com/timoalho/VQCDThermo.
  49. [49]
    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  50. [50]
    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
  51. [51]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].ADSGoogle Scholar
  52. [52]
    A.O. Starinets, Quasinormal spectrum and the black hole membrane paradigm, Phys. Lett. B 670 (2009) 442 [arXiv:0806.3797] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    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
  54. [54]
    D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  55. [55]
    J. Erdmenger, M. Kaminski and F. Rust, Holographic vector mesons from spectral functions at finite baryon or isospin density, Phys. Rev. D 77 (2008) 046005 [arXiv:0710.0334] [INSPIRE].ADSGoogle Scholar
  56. [56]
    J. Erdmenger, M. Kaminski, P. Kerner and F. Rust, Finite baryon and isospin chemical potential in AdS/CFT with flavor, JHEP 11 (2008) 031 [arXiv:0807.2663] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    J. Erdmenger, M. Kaminski and F. Rust, QGP thermodynamics and meson spectroscopy with AdS/CFT, PoS(CONFINEMENT8)131 [arXiv:0901.2456] [INSPIRE].
  58. [58]
    J. Mas, J.P. Shock, J. Tarrio and D. Zoakos, Holographic spectral functions at finite baryon density, JHEP 09 (2008) 009 [arXiv:0805.2601] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  59. [59]
    K.-Y. Kim, S.-J. Sin and I. Zahed, Dense hadronic matter in holographic QCD, J. Korean Phys. Soc. 63 (2013) 1515 [hep-th/0608046] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    O. Aharony, K. Peeters, J. Sonnenschein and M. Zamaklar, Rho meson condensation at finite isospin chemical potential in a holographic model for QCD, JHEP 02 (2008) 071 [arXiv:0709.3948] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    B.S. DiNunno, M. Ihl, N. Jokela and J.F. Pedraza, Holographic zero sound at finite temperature in the Sakai-Sugimoto model, JHEP 04 (2014) 149 [arXiv:1403.1827] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    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
  63. [63]
    J. Mas, J.P. Shock and J. Tarrio, A note on conductivity and charge diffusion in holographic flavour systems, JHEP 01 (2009) 025 [arXiv:0811.1750] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  65. [65]
    C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetMATHGoogle Scholar
  66. [66]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    B.B. Brandt, A. Francis, M. Laine and H.B. Meyer, Vector screening masses in the quark-gluon plasma and their physical significance, Nucl. Phys. A 931 (2014) 861 [arXiv:1408.5917] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    B.B. Brandt, A. Francis, H.B. Meyer and H. Wittig, Thermal correlators in the ρ channel of two-flavor QCD, JHEP 03 (2013) 100 [arXiv:1212.4200] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    C.-H. Lee and I. Zahed, Electromagnetic radiation in hot QCD matter: rates, electric conductivity, flavor susceptibility and diffusion, Phys. Rev. C 90 (2014) 025204 [arXiv:1403.1632] [INSPIRE].ADSGoogle Scholar
  70. [70]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].ADSGoogle Scholar
  71. [71]
    Y. Qian and I. Zahed, \( \mathcal{P} \) -odd pion azimuthal charge correlations in heavy ion collisions, arXiv:1205.2366 [INSPIRE].

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of Physics and AstronomyStony Brook UniversityStony BrookUnited States

Personalised recommendations