Abstract
A holographic model of QCD in the limit of large number of colors, Nc, and massless fermion flavors, Nf , but constant ratio xf = Nf /Nc is analyzed at finite temperature and chemical potential. The five dimensional gravity model contains three bulk fields: a scalar dilaton sourcing TrF2, a scalar tachyon dual to \( \overline{q}q \) and a 4-vector dual to the baryon current \( \overline{q} \)γμ q. The main result is the μ, T phase diagram of the holographic theory. A first order deconfining transition along Th(μ) and a chiral transition at Tχ(μ) > Th(μ) are found. The chiral transition is of second order for small μ and becomes of first order at larger μ. The two regimes are separated by a tricritical point. The dependence of thermodynamical quantities including the speed of sound and susceptibilities on the chemical potential and temperature is computed. A new quantum critical regime is found at zero temperature and finite chemical potential. It is controlled by an AdS2 × R3 geometry and displays semi-local criticality.
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References
J. Kogut and M. Stephanov, The phases of quantum chromodynamics: from confinement to extreme environments, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol.21 (2004) 1 [INSPIRE].
O. Scavenius, A. Mócsy , I.N. Mishustin and D.H. Rischke, Chiral phase transition within effective models with constituent quarks, Phys. Rev.C 64 (2001) 045202 [nucl-th/0007030] [INSPIRE].
T. Kahara and K. Tuominen, Degrees of freedom and the phase transitions of two flavor QCD, Phys. Rev.D 78 (2008) 034015 [arXiv:0803.2598] [INSPIRE].
M.A. Stephanov, QCD phase diagram and the critical point, Prog. Theor. Phys. Suppl.153 (2004) 139 [Int. J. Mod. Phys.A 20 (2005) 4387] [hep-ph/0402115] [INSPIRE].
R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP06 (2009) 006 [arXiv:0903.2834] [INSPIRE].
O. DeWolfe, S.S. Gubser and C. Rosen, A holographic critical point, Phys. Rev.D 83 (2011) 086005 [arXiv:1012.1864] [INSPIRE].
O. DeWolfe, S.S. Gubser and C. Rosen, Dynamic critical phenomena at a holographic critical point, Phys. Rev.D 84 (2011) 126014 [arXiv:1108.2029] [INSPIRE].
O. Kaczmarek et al., Phase boundary for the chiral transition in (2 + 1)-flavor QCD at small values of the chemical potential, Phys. Rev.D 83 (2011) 014504 [arXiv:1011.3130] [INSPIRE].
F. Karsch, B.-J. Schaefer, M. Wagner and J. Wambach, Towards finite density QCD with Taylor expansions, Phys. Lett.B 698 (2011) 256 [arXiv:1009.5211] [INSPIRE].
G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The QCD phase diagram at nonzero quark density, JHEP04 (2011) 001 [arXiv:1102.1356] [INSPIRE].
P. de Forcrand and O. Philipsen, The curvature of the critical surface (mu,d , ms)crit(μ): a progress report, PoS(LATTICE 2008)208 [arXiv:0811.3858] [INSPIRE].
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].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [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].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav.26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys.A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: part I, JHEP02 (2008) 032 [arXiv:0707.1324] [INSPIRE].
U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: part II, JHEP02 (2008) 019 [arXiv:0707.1349] [INSPIRE].
U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved holographic QCD, Lect. Notes Phys.828 (2011) 79 [arXiv:1006.5461] [INSPIRE].
U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and thermodynamics of 5D dilaton-gravity, JHEP05 (2009) 033 [arXiv:0812.0792] [INSPIRE].
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].
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].
M. Järvinen and F. Sannino, Holographic conformal window — a bottom up approach, JHEP05 (2010) 041 [arXiv:0911.2462] [INSPIRE].
J. Alanen and K. Kajantie, Thermodynamics of a field theory with infrared fixed point from gauge/gravity duality, Phys. Rev.D 81 (2010) 046003 [arXiv:0912.4128] [INSPIRE].
J. Alanen, K. Kajantie and K. Tuominen, Thermodynamics of quasi conformal theories from gauge/gravity duality, Phys. Rev.D 82 (2010) 055024 [arXiv:1003.5499] [INSPIRE].
J. Alanen, T. Alho, K. Kajantie and K. Tuominen, Mass spectrum and thermodynamics of quasi-conformal gauge theories from gauge/gravity duality, Phys. Rev.D 84 (2011) 086007 [arXiv:1107.3362] [INSPIRE].
F. Bigazzi, R. Casero, A.L. Cotrone, E. Kiritsis and A. Paredes, Non-critical holography and four-dimensional CFT’s with fundamentals, JHEP10 (2005) 012 [hep-th/0505140] [INSPIRE].
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].
I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from Sen’s tachyon action, Phys. Rev.D 81 (2010) 115004 [arXiv:1003.2377] [INSPIRE].
I. Iatrakis, E. Kiritsis and A. Paredes, An AdS/QCD model from tachyon condensation: II, JHEP11 (2010) 123 [arXiv:1010.1364] [INSPIRE].
I. Iatrakis and E. Kiritsis, Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate, JHEP02 (2012) 064 [arXiv:1109.1282] [INSPIRE].
D. Arean, I. Iatrakis, M. Järvinen and E. Kiritsis, The discontinuities of conformal transitions and mass spectra of V-QCD, JHEP11 (2013) 068 [arXiv:1309.2286] [INSPIRE].
M. Järvinen and E. Kiritsis, Holographic models for QCD in the Veneziano limit, JHEP03 (2012) 002 [arXiv:1112.1261] [INSPIRE].
T. Alho, M. Järvinen, K. Kajantie, E. Kiritsis and K. Tuominen, On finite-temperature holographic QCD in the Veneziano limit, JHEP01 (2013) 093 [arXiv:1210.4516] [INSPIRE].
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].
A. Stoffers and I. Zahed, Improved AdS/QCD model with matter, Phys. Rev.D 83 (2011) 055016 [arXiv:1009.4428] [INSPIRE].
B. Gouteraux and E. Kiritsis, Quantum critical lines in holographic phases with (un)broken symmetry, JHEP04 (2013) 053 [arXiv:1212.2625] [INSPIRE].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev.D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
T. Alho, Numerical code for thermodynamics of holographic V-QCD, https://github.com/timoalho/VQCDThermo.
B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
S.-X. Qin and D.H. Rischke, Quark spectral function and deconfinement at nonzero temperature, Phys. Rev.D 88 (2013) 056007 [arXiv:1304.6547] [INSPIRE].
A. Mócsy , F. Sannino and K. Tuominen, Confinement versus chiral symmetry, Phys. Rev. Lett.92 (2004) 182302 [hep-ph/0308135] [INSPIRE].
T. Kahara, M. Ruggieri and K. Tuominen, Deconfinement vs. chiral symmetry and higher representation matter, Phys. Rev.D 85 (2012) 094020 [arXiv:1202.1769] [INSPIRE].
S. Borsányi et al., Full result for the QCD equation of state with 2 + 1 flavors, Phys. Lett.B 730 (2014) 99 [arXiv:1309.5258] [INSPIRE].
R.D. Pisarski and F. Wilczek, Remarks on the chiral phase transition in chromodynamics, Phys. Rev.D 29 (1984) 338 [INSPIRE].
P. de Forcrand and O. Philipsen, The chiral critical line of Nf = 2 + 1 QCD at zero and non-zero baryon density, JHEP01 (2007) 077 [hep-lat/0607017] [INSPIRE].
A.J. Paterson, Coleman-Weinberg symmetry breaking in the chiral SU(N ) × SU(N ) linear σ-model, Nucl. Phys.B 190 (1981) 188 [INSPIRE].
P.B. Arnold and L.G. Yaffe, The ϵ-expansion and the electroweak phase transition, Phys. Rev.D 49 (1994) 3003 [Erratum ibid.D 55 (1997) 1114] [hep-ph/9312221] [INSPIRE].
K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at mH larger or equal to mW ?, Phys. Rev. Lett.77 (1996) 2887 [hep-ph/9605288] [INSPIRE].
J. Noronha, Connecting Polyakov loops to the thermodynamics of SU(Nc) gauge theories using the gauge-string duality, Phys. Rev.D 81 (2010) 045011 [arXiv:0910.1261] [INSPIRE].
J. Alanen, K. Kajantie and V. Suur-Uski, Spatial string tension of finite temperature QCD matter in gauge/gravity duality, Phys. Rev.D 80 (2009) 075017 [arXiv:0905.2032] [INSPIRE].
M. Spradlin and A. Strominger, Vacuum states for AdS2 black holes, JHEP11 (1999) 021 [hep-th/9904143] [INSPIRE].
K. Kajantie, M. Krssak and A. Vuorinen, Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory, JHEP05 (2013) 140 [arXiv:1302.1432] [INSPIRE].
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ArXiv ePrint: 1312.5199
http://hep.physics.uoc.gr/∼kiritsis/.
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A correction to this article is available at https://doi.org/10.1007/JHEP02(2015)033
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Alho, T., Järvinen, M., Kajantie, K. et al. A holographic model for QCD in the Veneziano limit at finite temperature and density. J. High Energ. Phys. 2014, 124 (2014). https://doi.org/10.1007/JHEP04(2014)124
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DOI: https://doi.org/10.1007/JHEP04(2014)124