Abstract
We discuss mesons in thermalizing gluon backgrounds in the \( \mathcal{N} \) = 2 super-symmetric QCD using the gravity dual. We numerically compute the dynamics of a probe D7-brane in the Vaidya-AdS geometry that corresponds to a D3-brane background thermalizing from zero to finite temperatures by energy injection. In static backgrounds, it has been known that there are two kinds of brane embeddings where the brane intersects the black hole or not. They correspond to the phases with melted or stable mesons. In our dynamical setup, we obtain three cases depending on final temperatures and injection time scales. The brane stays outside of the black hole horizon when the final temperature is low, while it intersects the horizon and settles down to the static equilibrium state when the final temperature is high. Between these two cases, we find the overeager case where the brane dynamically intersects the horizon although the final temperature is not high enough for a static brane to intersect the horizon. The interpretation of this phenomenon in the dual field theory is meson melting due to non-thermal effects caused by rapid energy injection. In addition, we comment on the late time evolution of the brane and a possibility of its reconnection.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
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].
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].
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].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
A. Buchel and J.T. Liu, Universality of the shear viscosity in supergravity, Phys. Rev. Lett. 93 (2004) 090602 [hep-th/0311175] [INSPIRE].
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].
R. Baier, P. Romatschke, D.T. Son, A.O. Starinets and M.A. Stephanov, Relativistic viscous hydrodynamics, conformal invariance and holography, JHEP 04 (2008) 100 [arXiv:0712.2451] [INSPIRE].
S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP 02 (2008) 045 [arXiv:0712.2456] [INSPIRE].
V.E. Hubeny, S. Minwalla and M. Rangamani, The fluid/gravity correspondence, arXiv:1107.5780 [INSPIRE].
S. Bhattacharyya and S. Minwalla, Weak Field Black Hole Formation in Asymptotically AdS Spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [INSPIRE].
V. Balasubramanian et al., Inhomogeneous Thermalization in Strongly Coupled Field Theories, Phys. Rev. Lett. 111 (2013) 231602 [arXiv:1307.1487] [INSPIRE].
V. Balasubramanian et al., Inhomogeneous holographic thermalization, JHEP 10 (2013) 082 [arXiv:1307.7086] [INSPIRE].
B. Craps et al., Gravitational collapse and thermalization in the hard wall model, JHEP 02 (2014) 120 [arXiv:1311.7560] [INSPIRE].
R.A. Janik and R.B. Peschanski, Gauge/gravity duality and thermalization of a boost-invariant perfect fluid, Phys. Rev. D 74 (2006) 046007 [hep-th/0606149] [INSPIRE].
P. Benincasa, A. Buchel, M.P. Heller and R.A. Janik, On the supergravity description of boost invariant conformal plasma at strong coupling, Phys. Rev. D 77 (2008) 046006 [arXiv:0712.2025] [INSPIRE].
G. Beuf, M.P. Heller, R.A. Janik and R. Peschanski, Boost-invariant early time dynamics from AdS/CFT, JHEP 10 (2009) 043 [arXiv:0906.4423] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, The characteristics of thermalization of boost-invariant plasma from holography, Phys. Rev. Lett. 108 (2012) 201602 [arXiv:1103.3452] [INSPIRE].
M.P. Heller, R.A. Janik and P. Witaszczyk, A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization — an ADM formulation, Phys. Rev. D 85 (2012) 126002 [arXiv:1203.0755] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
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].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Meson spectroscopy in AdS/CFT with flavor, JHEP 07 (2003) 049 [hep-th/0304032] [INSPIRE].
C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Holographic meson melting, JHEP 04 (2007) 031 [hep-th/0612169] [INSPIRE].
R.C. Myers, A.O. Starinets and R.M. Thomson, Holographic spectral functions and diffusion constants for fundamental matter, JHEP 11 (2007) 091 [arXiv:0706.0162] [INSPIRE].
I. Kirsch, Generalizations of the AdS/CFT correspondence, Fortsch. Phys. 52 (2004) 727 [hep-th/0406274] [INSPIRE].
K. Ghoroku, T. Sakaguchi, N. Uekusa and M. Yahiro, Flavor quark at high temperature from a holographic model, Phys. Rev. D 71 (2005) 106002 [hep-th/0502088] [INSPIRE].
R. Apreda, J. Erdmenger, N. Evans and Z. Guralnik, Strong coupling effective Higgs potential and a first order thermal phase transition from AdS/CFT duality, Phys. Rev. D 71 (2005) 126002 [hep-th/0504151] [INSPIRE].
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].
T. Albash, V.G. Filev, C.V. Johnson and A. Kundu, A topology-changing phase transition and the dynamics of flavour, Phys. Rev. D 77 (2008) 066004 [hep-th/0605088] [INSPIRE].
D. Mateos, R.C. Myers and R.M. Thomson, Thermodynamics of the brane, JHEP 05 (2007) 067 [hep-th/0701132] [INSPIRE].
M. Kruczenski, D. Mateos, R.C. Myers and D.J. Winters, Towards a holographic dual of large-N c QCD, JHEP 05 (2004) 041 [hep-th/0311270] [INSPIRE].
N. Evans, T. Kalaydzhyan, K.-Y. Kim and I. Kirsch, Non-equilibrium physics at a holographic chiral phase transition, JHEP 01 (2011) 050 [arXiv:1011.2519] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
J. Abajo-Arrastia, J. Aparicio and E. Lopez, Holographic Evolution of Entanglement Entropy, JHEP 11 (2010) 149 [arXiv:1006.4090] [INSPIRE].
T. Albash and C.V. Johnson, Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches, New J. Phys. 13 (2011) 045017 [arXiv:1008.3027] [INSPIRE].
V. Balasubramanian et al., Thermalization of Strongly Coupled Field Theories, Phys. Rev. Lett. 106 (2011) 191601 [arXiv:1012.4753] [INSPIRE].
V. Balasubramanian et al., Holographic Thermalization, Phys. Rev. D 84 (2011) 026010 [arXiv:1103.2683] [INSPIRE].
A.J. Amsel, D. Marolf and A. Virmani, Collisions with Black Holes and Deconfined Plasmas, JHEP 04 (2008) 025 [arXiv:0712.2221] [INSPIRE].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [INSPIRE].
D. Garfinkle and L.A. Pando Zayas, Rapid Thermalization in Field Theory from Gravitational Collapse, Phys. Rev. D 84 (2011) 066006 [arXiv:1106.2339] [INSPIRE].
D. Garfinkle, L.A. Pando Zayas and D. Reichmann, On Field Theory Thermalization from Gravitational Collapse, JHEP 02 (2012) 119 [arXiv:1110.5823] [INSPIRE].
B. Wu, On holographic thermalization and gravitational collapse of massless scalar fields, JHEP 10 (2012) 133 [arXiv:1208.1393] [INSPIRE].
S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].
A. Buchel, R.C. Myers and A. van Niekerk, Universality of Abrupt Holographic Quenches, Phys. Rev. Lett. 111 (2013) 201602 [arXiv:1307.4740] [INSPIRE].
C. Barcelo, S. Liberati, S. Sonego and M. Visser, Minimal conditions for the existence of a Hawking-like flux, Phys. Rev. D 83 (2011) 041501 [arXiv:1011.5593] [INSPIRE].
S. Kinoshita and N. Tanahashi, Hawking temperature for near-equilibrium black holes, Phys. Rev. D 85 (2012) 024050 [arXiv:1111.2684] [INSPIRE].
S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [INSPIRE].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
A. Flachi and T. Tanaka, Escape of black holes from the brane, Phys. Rev. Lett. 95 (2005) 161302 [hep-th/0506145] [INSPIRE].
A. Flachi, O. Pujolàs, M. Sasaki and T. Tanaka, Black holes escaping from domain walls, Phys. Rev. D 73 (2006) 125017 [hep-th/0601174] [INSPIRE].
A. Flachi, O. Pujolàs, M. Sasaki and T. Tanaka, Critical escape velocity of black holes from branes, Phys. Rev. D 74 (2006) 045013 [hep-th/0604139] [INSPIRE].
A. Flachi and T. Tanaka, Branes and Black holes in Collision, Phys. Rev. D 76 (2007) 025007 [hep-th/0703019] [INSPIRE].
B. Carter, Equations of motion of a stiff geodynamic string or higher brane, Class. Quant. Grav. 11 (1994) 2677 [INSPIRE].
B. Carter and R. Gregory, Curvature corrections to dynamics of domain walls, Phys. Rev. D 51 (1995) 5839 [hep-th/9410095] [INSPIRE].
V.P. Frolov and D. Gorbonos, A Toy Model for Topology Change Transitions: Role of Curvature Corrections, Phys. Rev. D 79 (2009) 024006 [arXiv:0808.3024] [INSPIRE].
V.G. Czinner and A. Flachi, Thickness perturbations and topology change transitions in brane: black hole systems, Phys. Rev. D 80 (2009) 104017 [arXiv:0908.2957] [INSPIRE].
V.G. Czinner, Thick brane solutions and topology change transition on black hole backgrounds, Phys. Rev. D 82 (2010) 024035 [arXiv:1006.4424] [INSPIRE].
V.P. Frolov, Merger Transitions in Brane-Black-Hole Systems: Criticality, Scaling and Self-Similarity, Phys. Rev. D 74 (2006) 044006 [gr-qc/0604114] [INSPIRE].
K. Murata, S. Kinoshita and N. Tanahashi, Non-equilibrium Condensation Process in a Holographic Superconductor, JHEP 07 (2010) 050 [arXiv:1005.0633] [INSPIRE].
M.J. Bhaseen, J.P. Gauntlett, B.D. Simons, J. Sonner and T. Wiseman, Holographic Superfluids and the Dynamics of Symmetry Breaking, Phys. Rev. Lett. 110 (2013) 015301 [arXiv:1207.4194] [INSPIRE].
G.F. Carrier, M. Krook and C.E. Pearson, Functions of a complex variable — theory and technique. Society for Industrial and Applied Mathematics, (2005).
A.D. Rendall, Reduction of the characteristic initial value problem to the cauchy problem and its applications to the einstein equations, Proc. Roy. Soc. Lond. A 427 (1990) 221.
H.-O. Kreiss and J. Winicour, The well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves, Class. Quant. Grav. 28 (2011) 145020 [arXiv:1010.1201] [INSPIRE].
M.C. Babiuc, H.-O. Kreiss and J. Winicour, Testing the well-posedness of characteristic evolution of scalar waves, Class. Quant. Grav. 31 (2014) 025022 [arXiv:1305.7179] [INSPIRE].
D. Hilditch, An introduction to well-posedness and free-evolution, Int. J. Mod. Phys. A 28 (2013) 1340015 [arXiv:1309.2012] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1401.5106
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Ishii, T., Kinoshita, S., Murata, K. et al. Dynamical meson melting in holography. J. High Energ. Phys. 2014, 99 (2014). https://doi.org/10.1007/JHEP04(2014)099
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2014)099