Abstract
We study finite temperature \( \mathcal{N}=4 \) Super Yang-Mills (and more general gauge theories realized on intersecting D3-D7 branes) in the presence of dynamical massless fundamental matter fields at finite baryon charge density. We construct the holographic dual charged black hole solutions at first order in the flavor backreaction but exact in the charge density. The thermodynamical properties of the dual gauge theories coincide with the ones found in the usual charged D7-probe limit and the system turns out to be thermodynamically stable. By analyzing the higher order correction in the flavor backreaction, we provide a novel argument for the un-reliability of the charged probe approximation (and the present solution) in the extremality limit, i.e. at zero temperature.
We then consider scalar mesonic-like bound states, whose spectrum is dual to that of linearized fluctuations of D7-brane worldvolume fields around our gravity backgrounds. In particular we focus on a scalar field saturating the Breitenlohner-Freedman bound in the flavorless limit, and coupled to fields dual to irrelevant operators. By looking at quasinormal modes of this scalar, we find no signals of instabilities in the regime of validity of the solutions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
S.P. Kumar, Heavy quark density in N = 4 SYM: from hedgehog to Lifshitz spacetimes, JHEP 08 (2012) 155 [arXiv:1206.5140] [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].
T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].
M. Ammon, J. Erdmenger, S. Lin, S. Muller, A. O’Bannon and J.P. Shock, On Stability and Transport of Cold Holographic Matter, JHEP 09 (2011) 030 [arXiv:1108.1798] [INSPIRE].
A. Karch and E. Katz, Adding flavor to AdS/CFT, JHEP 06 (2002) 043 [hep-th/0205236] [INSPIRE].
M. Graña and J. Polchinski, Gauge/gravity duals with holomorphic dilaton, Phys. Rev. D 65 (2002) 126005 [hep-th/0106014] [INSPIRE].
M. Bertolini, P. Di Vecchia, M. Frau, A. Lerda and R. Marotta, N=2 gauge theories on systems of fractional D3/D7 branes, Nucl. Phys. B 621 (2002) 157 [hep-th/0107057] [INSPIRE].
B.A. Burrington, J.T. Liu, L.A. Pando Zayas and D. Vaman, Holographic duals of flavored N =1 super Yang-Mills: Beyond the probe approximation, JHEP 02(2005) 022 [hep-th/0406207] [INSPIRE].
I. Kirsch and D. Vaman, The D3/D7 background and flavor dependence of Regge trajectories, Phys. Rev. D 72 (2005) 026007 [hep-th/0505164] [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].
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].
A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: Some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].
D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv:0709.1225] [INSPIRE].
D. Mateos and L. Patino, Bright branes for strongly coupled plasmas, JHEP 11 (2007) 025 [arXiv:0709.2168] [INSPIRE].
R.C. Myers and A. Sinha, The Fast life of holographic mesons, JHEP 06 (2008) 052 [arXiv:0804.2168] [INSPIRE].
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].
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].
M. Ammon, K. Jensen, K.-Y. Kim, J.N. Laia and A. O’Bannon, Moduli Spaces of Cold Holographic Matter, JHEP 11 (2012) 055 [arXiv:1208.3197] [INSPIRE].
J. Erdmenger, N. Evans, I. Kirsch and E. Threlfall, Mesons in Gauge/Gravity Duals - A Review, Eur. Phys. J. A 35 (2008) 81 [arXiv:0711.4467] [INSPIRE].
F. Bigazzi, R. Casero, A. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP 10 (2005) 012 [hep-th/0505140] [INSPIRE].
R. Casero, C. Núñez and A. Paredes, Towards the string dual of N = 1 SQCD-like theories, Phys. Rev. D 73 (2006) 086005 [hep-th/0602027] [INSPIRE].
F. Benini, F. Canoura, S. Cremonesi, C. Núñez and A.V. Ramallo, Unquenched flavors in the Klebanov-Witten model, JHEP 02 (2007) 090 [hep-th/0612118] [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, A. Paredes, A.V. Ramallo and J. Tarrio, D3-D7 quark-gluon Plasmas, JHEP 11 (2009) 117 [arXiv:0909.2865] [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, D. Mayerson and J. Tarrio, D3-D7 quark-gluon Plasmas at Finite Baryon Density, JHEP 04 (2011) 060 [arXiv:1101.3560] [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, D. Mayerson and J. Tarrio, Holographic Duals of Quark Gluon Plasmas with Unquenched Flavors, Commun. Theor. Phys. 57 (2012) 364 [arXiv:1110.1744] [INSPIRE].
F. Bigazzi, A.L. Cotrone and J. Tarrio, Hydrodynamics of fundamental matter, JHEP 02 (2010) 083 [arXiv:0912.3256] [INSPIRE].
F. Bigazzi and A.L. Cotrone, An elementary stringy estimate of transport coefficients of large temperature QCD, JHEP 08 (2010) 128 [arXiv:1006.4634] [INSPIRE].
A. Magana, J. Mas, L. Mazzanti and J. Tarrio, Probes on D3-D7 quark-gluon Plasmas, JHEP 07 (2012) 058 [arXiv:1205.6176] [INSPIRE].
A.L. Cotrone and J. Tarrio, Consistent reduction of charged D3-D7 systems, JHEP 10 (2012) 164 [arXiv:1207.6703] [INSPIRE].
D. Cassani, G. Dall’Agata and A.F. Faedo, Type IIB supergravity on squashed Sasaki-Einstein manifolds, JHEP 05 (2010) 094 [arXiv:1003.4283] [INSPIRE].
J.T. Liu, P. Szepietowski and Z. Zhao, Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds, Phys. Rev. D 81 (2010) 124028 [arXiv:1003.5374] [INSPIRE].
J.P. Gauntlett and O. Varela, Universal Kaluza-Klein reductions of type IIB to N = 4 supergravity in five dimensions, JHEP 06 (2010) 081 [arXiv:1003.5642] [INSPIRE].
A. Ceresole, G. Dall’Agata, R. D’Auria and S. Ferrara, Spectrum of type IIB supergravity on AdS 5 × T 11 : Predictions on N = 1 SCFT’s, Phys. Rev. D 61 (2000) 066001 [hep-th/9905226] [INSPIRE].
S. Benvenuti, M. Mahato, L.A. Pando Zayas and Y. Tachikawa, The Gauge/gravity theory of blown up four cycles, hep-th/0512061 [INSPIRE].
F. Bigazzi, A.L. Cotrone, A. Paredes and A.V. Ramallo, Screening effects on meson masses from holography, JHEP 05 (2009) 034 [arXiv:0903.4747] [INSPIRE].
H. Chamblin and H. Reall, Dynamic dilatonic domain walls, Nucl. Phys. B 562 (1999) 133 [hep-th/9903225] [INSPIRE].
S.S. Gubser, S.S. Pufu and F.D. Rocha, Bulk viscosity of strongly coupled plasmas with holographic duals, JHEP 08 (2008) 085 [arXiv:0806.0407] [INSPIRE].
S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [INSPIRE].
S.S. Pal, Fermi-like Liquid From Einstein-DBI-Dilaton System, JHEP 04 (2013) 007 [arXiv:1209.3559] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, World-Volume Effective Theory for Higher-Dimensional Black Holes, Phys. Rev. Lett. 102 (2009) 191301 [arXiv:0902.0427] [INSPIRE].
R. Emparan, T. Harmark, V. Niarchos and N.A. Obers, Essentials of Blackfold Dynamics, JHEP 03 (2010) 063 [arXiv:0910.1601] [INSPIRE].
M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
K. Skenderis, Lecture notes on holographic renormalization, Class. Quant. Grav. 19 (2002) 5849 [hep-th/0209067] [INSPIRE].
B.C. van Rees, Holographic renormalization for irrelevant operators and multi-trace counterterms, JHEP 08 (2011) 093 [arXiv:1102.2239] [INSPIRE].
A.O. Starinets, Quasinormal modes of near extremal black branes, Phys. Rev. D 66 (2002) 124013 [hep-th/0207133] [INSPIRE].
S. Musiri and G. Siopsis, Asymptotic form of quasinormal modes of large AdS black holes, Phys. Lett. B 576 (2003) 309 [hep-th/0308196] [INSPIRE].
A. Karch, A. O’Bannon and K. Skenderis, Holographic renormalization of probe D-branes in AdS/CFT, JHEP 04 (2006) 015 [hep-th/0512125] [INSPIRE].
S.K. Domokos and J.A. Harvey, Baryon number-induced Chern-Simons couplings of vector and axial-vector mesons in holographic QCD, Phys. Rev. Lett. 99 (2007) 141602 [arXiv:0704.1604] [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
A. Karch, A. O’Bannon and E. Thompson, The Stress-Energy Tensor of Flavor Fields from AdS/CFT, JHEP 04 (2009) 021 [arXiv:0812.3629] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1304.4802
Rights and permissions
About this article
Cite this article
Bigazzi, F., Cotrone, A.L. & Tarrío, J. Charged D3-D7 plasmas: novel solutions, extremality and stability issues. J. High Energ. Phys. 2013, 74 (2013). https://doi.org/10.1007/JHEP07(2013)074
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2013)074