Caselle, Michele; Castagnini, Luca; Feo, Alessandra; Gliozzi, Ferdinando; Panero, Marco Thermodynamics of \(\mathrm{SU}(N)\) Yang-Mills theories in \(2 + 1\) dimensions I – the confining phase. (English) Zbl 1301.81113 J. High Energy Phys. 2011, No. 6, Paper No. 142, 24 p. (2011). Summary: We compute the equation of state in the confining phase of \(\mathrm{SU}(N)\) Yang-Mills theories with \(N =\) 2, 3, 4, 5 and 6 colors in \(2 + 1\) dimensions, via lattice simulations. At low enough temperatures, the results are accurately described by a gas of glueballs, including all known states below the two-particle threshold. Close to the deconfinement temperature, however, this prediction underestimates the numerical results, and the contribution from heavier glueballs has to be included. We show that the spectral density of the latter can be accurately described using a simple bosonic string model. Cited in 5 Documents MSC: 81T13 Yang-Mills and other gauge theories in quantum field theory 81T25 Quantum field theory on lattices 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 81V05 Strong interaction, including quantum chromodynamics 81T28 Thermal quantum field theory 82B30 Statistical thermodynamics Keywords:field theories in lower dimensions; lattice gauge field theories; \(1/N\) expansion Software:Chroma PDFBibTeX XMLCite \textit{M. Caselle} et al., J. High Energy Phys. 2011, No. 6, Paper No. 142, 24 p. (2011; Zbl 1301.81113) Full Text: DOI arXiv References: [1] N. Cabibbo and G. Parisi, Exponential hadronic spectrum and quark liberation, Phys. Lett.B 59 (1975) 67 [SPIRES]. [2] J.C. Collins and M.J. Perry, Superdense matter: neutrons or asymptotically free quarks?, Phys. Rev. Lett.34 (1975) 1353 [SPIRES]. [3] A.D. Linde, Infrared problem in thermodynamics of the Yang-Mills gas, Phys. Lett.B 96 (1980) 289 [SPIRES]. [4] D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys.53 (1981) 43 [SPIRES]. [5] M. Cheng et al., Equation of state for physical quark masses, Phys. Rev.D 81 (2010) 054504 [arXiv:0911.2215] [SPIRES]. [6] S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP11 (2010) 077 [arXiv:1007.2580] [SPIRES]. · Zbl 1294.81269 [7] S. Gupta, QCD at finite density, PoSLATTICE2010 (2010) 007 [arXiv:1101.0109] [SPIRES]. [8] K. Kanaya, Finite temperature QCD on the lattice — status 2010, PoSLATTICE2010 (2010) 012 [arXiv:1012.4247] [SPIRES]. [9] C. De Tar, QCD thermodynamics on the lattice: recent results, arXiv:1101.0208 [SPIRES]. · Zbl 1196.81232 [10] U.W. Heinz and M. Jacob, Evidence for a new state of matter: an assessment of the results from the CERN lead beam programme, nucl-th/0002042 [SPIRES]. [11] M. Gyulassy and L. McLerran, New forms of QCD matter discovered at RHIC, Nucl. Phys.A 750 (2005) 30 [nucl-th/0405013] [SPIRES]. [12] PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: experimental evaluation by the PHENIX collaboration, Nucl. Phys.A 757 (2005) 184 [nucl-ex/0410003] [SPIRES]. [13] BRAHMS collaboration, I. Arsene et al., Quark gluon plasma an color glass condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys.A 757 (2005) 1 [nucl-ex/0410020] [SPIRES]. [14] B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys.A 757 (2005) 28 [nucl-ex/0410022] [SPIRES]. [15] STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: the STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys.A 757 (2005) 102 [nucl-ex/0501009] [SPIRES]. [16] ATLAS collaboration, G. Aad et al., Observation of a centrality-dependent dijet asymmetry in lead-lead collisions at \(\sqrt{{{S_{NN}}}} = 2.76\) TeV with the ATLAS detector at the LHC, Phys. Rev. Lett.105 (2010) 252303 [arXiv:1011.6182] [SPIRES]. [17] CMS collaboration, S. Chatrchyan et al., Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV, arXiv:1102.1957 [SPIRES]. [18] The ALICE collaboration, K. Aamodt et al., Elliptic flow of charged particles in Pb-Pb collisions at 2.76 TeV, Phys. Rev. Lett.105 (2010) 252302 [arXiv:1011.3914] [SPIRES]. [19] The ALICE collaboration, B. Abelev et al., Charged-particle multiplicity density at mid-rapidity in central Pb-Pb collisions at \(\sqrt{{{s_{NN}}}} = 2.76\) TeV, Phys. Rev. Lett.105 (2010) 252301 [arXiv:1011.3916] [SPIRES]. [20] ALICE collaboration, K. Aamodt et al., Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at \(\sqrt{{{s_{NN}}}} = 2.76\) TeV, Phys. Lett.B 696 (2011) 30 [arXiv:1012.1004] [SPIRES]. [21] ALICE collaboration, K. Aamodt et al., Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at \(\sqrt{{{s_{NN}}}} = 2.76\) TeV, Phys. Rev. Lett.106 (2011) 032301 [arXiv:1012.1657] [SPIRES]. [22] ALICE collaboration, K. Aamodt et al., Two-pion Bose-Einstein correlations in central PbPb collisions at \(\sqrt{{{s_{NN}}}} = 2.76\) TeV, Phys. Lett.B 696 (2011) 328 [arXiv:1012.4035] [SPIRES]. [23] A. Andronic, P. Braun-Munzinger and J. Stachel, Thermal hadron production in relativistic nuclear collisions, Acta Phys. Polon.B 40 (2009) 1005 [arXiv:0901.2909] [SPIRES]. [24] R. Hagedorn, Statistical thermodynamics of strong interactions at high energies, Nuovo Cim. Suppl.3 (1965) 147. [25] R. Hagedorn and J. Rafelski, Hot hadronic matter and nuclear collisions, Phys. Lett.B 97 (1980) 136 [SPIRES]. [26] C.J. Morningstar and M.J. Peardon, The glueball spectrum from an anisotropic lattice study, Phys. Rev.D 60 (1999) 034509 [hep-lat/9901004] [SPIRES]. [27] H.B. Meyer and M.J. Teper, Glueball Regge trajectories in (2 + 1) dimensional gauge theories, Nucl. Phys.B 668 (2003) 111 [hep-lat/0306019] [SPIRES]. · Zbl 1031.81555 [28] H.B. Meyer, Glueball Regge trajectories, hep-lat/0508002 [SPIRES]. · Zbl 1031.81555 [29] B. Lucini, A. Rago and E. Rinaldi, Glueball masses in the large-N limit, JHEP08 (2010) 119 [arXiv:1007.3879] [SPIRES]. · Zbl 1290.81074 [30] R.W. Johnson and M.J. Teper, String models of glueballs and the spectrum of SU(N) gauge theories in 2 + 1 dimensions, Phys. Rev.D 66 (2002) 036006 [hep-ph/0012287] [SPIRES]. [31] N. Isgur and J.E. Paton, A flux tube model for hadrons in QCD, Phys. Rev.D 31 (1985) 2910 [SPIRES]. [32] G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys.B 72 (1974) 461 [SPIRES]. [33] E. Witten, Baryons in the 1/n Expansion, Nucl. Phys.B 160 (1979) 57 [SPIRES]. [34] A.V. Manohar, Large-N QCD, hep-ph/9802419 [SPIRES]. [35] Y. Makeenko, Large-N gauge theories, hep-th/0001047 [SPIRES]. · Zbl 0986.81509 [36] O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [SPIRES]. [37] 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] [SPIRES]. · Zbl 0969.81047 [38] S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [SPIRES]. · Zbl 1355.81126 [39] E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [SPIRES]. · Zbl 0914.53048 [40] T.D. Cohen and V. Krejˇciˇrík, The Hagedorn spectrum and large-N c QCD in 2 + 1 and 3 + 1 dimensions, arXiv:1104.4783 [SPIRES]. [41] M.J. Teper, SU(N) gauge theories in 2 + 1 dimensions, Phys. Rev.D 59 (1999) 014512 [hep-lat/9804008] [SPIRES]. [42] M. Teper, Large-N and confining flux tubes as strings — a view from the lattice, Acta Phys. Polon.B 40 (2009) 3249 [arXiv:0912.3339] [SPIRES]. [43] H.B. Meyer, High-precision thermodynamics and Hagedorn density of states, Phys. Rev.D 80 (2009) 051502 [arXiv:0905.4229] [SPIRES]. [44] B. Lucini, M. Teper and U. Wenger, The deconfinement transition in SU(N) gauge theories, Phys. Lett.B 545 (2002) 197 [hep-lat/0206029] [SPIRES]. · Zbl 0998.81058 [45] B. Lucini, M. Teper and U. Wenger, The high temperature phase transition in SU(N) gauge theories, JHEP01 (2004) 061 [hep-lat/0307017] [SPIRES]. [46] B. Lucini, M. Teper and U. Wenger, Topology of SU(N) gauge theories at T ≈ 0 and T ≈ Tc, Nucl. Phys.B 715 (2005) 461 [hep-lat/0401028] [SPIRES]. · Zbl 1207.81074 [47] B. Lucini, M. Teper and U. Wenger, Properties of the deconfining phase transition in SU(N) gauge theories, JHEP02 (2005) 033 [hep-lat/0502003] [SPIRES]. [48] B. Bringoltz and M. Teper, The pressure of the SU(N) lattice gauge theory at large-N, Phys. Lett.B 628 (2005) 113 [hep-lat/0506034] [SPIRES]. [49] B. Bringoltz and M. Teper, In search of a Hagedorn transition in SU(N) lattice gauge theories at large-N, Phys. Rev.D 73 (2006) 014517 [hep-lat/0508021] [SPIRES]. [50] M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett.103 (2009) 232001 [arXiv:0907.3719] [SPIRES]. [51] M. Panero, Thermodynamics of the strongly interacting gluon plasma in the large-N limit, PoSLAT2009 (2009) 172 [arXiv:0912.2448] [SPIRES]. [52] S. Datta and S. Gupta, Scaling and the continuum limit of gluoNcplasmas, Phys. Rev.D 80 (2009) 114504 [arXiv:0909.5591] [SPIRES]. [53] S. Datta and S. Gupta, Continuum thermodynamics of the GluoNcplasma, Phys. Rev.D 82 (2010) 114505 [arXiv:1006.0938] [SPIRES]. [54] G. Boyd et al., Thermodynamics of SU(3) lattice gauge theory, Nucl. Phys.B 469 (1996) 419 [hep-lat/9602007] [SPIRES]. [55] S. Borsányi, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabó, Lattice SU(3) thermodynamics and the onset of perturbative behaviour, arXiv:1104.0013 [SPIRES]. [56] D.T. Son and A.O. Starinets, Viscosity, black holes and quantum field theory, Ann. Rev. Nucl. Part. Sci.57 (2007) 95 [arXiv:0704.0240] [SPIRES]. [57] D. Mateos, String theory and quantum chromodynamics, Class. Quant. Grav.24 (2007) S713 [arXiv:0709.1523] [SPIRES]. · Zbl 1128.81023 [58] 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] [SPIRES]. [59] S.S. Gubser and A. Karch, From gauge-string duality to strong interactions: a pedestrian’s guide, Ann. Rev. Nucl. Part. Sci.59 (2009) 145 [arXiv:0901.0935] [SPIRES]. [60] 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] [SPIRES]. [61] 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] [SPIRES]. · Zbl 1194.81333 [62] J. Alanen, K. Kajantie and V. Suur-Uski, A gauge/gravity duality model for gauge theory thermodynamics, Phys. Rev.D 80 (2009) 126008 [arXiv:0911.2114] [SPIRES]. [63] O. Andreev and V.I. Zakharov, The spatial string tension, thermal phase transition and AdS/QCD, Phys. Lett.B 645 (2007) 437 [hep-ph/0607026] [SPIRES]. · Zbl 1273.81177 [64] O. Andreev, Some thermodynamic aspects of pure glue, fuzzy bags and gauge/string duality, Phys. Rev.D 76 (2007) 087702 [arXiv:0706.3120] [SPIRES]. [65] E. Megías, H.J. Pirner and K. Veschgini, QCD-thermodynamics using 5-dim gravity, Phys. Rev.D 83 (2011) 056003 [arXiv:1009.2953] [SPIRES]. [66] K. Veschgini, E. Megias and H.J. Pirner, Trouble finding the optimal AdS/QCD, Phys. Lett.B 696 (2011) 495 [arXiv:1009.4639] [SPIRES]. [67] A. Peshier, B. Kämpfer, O.P. Pavlenko and G. Soff, A massive quasiparticle model of the SU(3) gluon plasma, Phys. Rev.D 54 (1996) 2399 [SPIRES]. [68] F. Buisseret and G. Lacroix, A minimal quasiparticle approach for the QGP and its large-N c limits, Eur. Phys. J.C 70 (2010) 1051 [arXiv:1006.0655] [SPIRES]. [69] F. Buisseret and G. Lacroix, Comments on Yang-Mills thermodynamics, the Hagedorn spectrum and the gluon gas, arXiv:1105.1092 [SPIRES]. [70] F. Giacosa, Analytical study of a gas of gluonic quasiparticles at high temperature: effective mass, pressure and trace anomaly, Phys. Rev.D 83 (2011) 114002 [arXiv:1009.4588] [SPIRES]. [71] P. Castorina, D.E. Miller and H. Satz, Trace anomaly and quasi-particles in finite temperature SU(N) gauge theory, Eur. Phys. J.C 71 (2011) 1673 [arXiv:1101.1255] [SPIRES]. [72] P. Castorina, V. Greco, D. Jaccarino and D. Zappalà, A reanalysis of finite temperature SU(N) gauge theory, arXiv:1105.5902 [SPIRES]. [73] P. Bialas, L. Daniel, A. Morel and B. Petersson, Thermodynamics of SU(3) gauge theory in 2 + 1 dimensions, Nucl. Phys.B 807 (2009) 547 [arXiv:0807.0855] [SPIRES]. · Zbl 1192.81227 [74] M. Caselle, L. Castagnini, A. Feo, F. Gliozzi and M. Panero, Thermodynamics of SU(N) gauge theories in 2 + 1 dimensions in the T < Tcregime, PoSLATTICE2010 (2010) 184 [arXiv:1011.4883] [SPIRES]. [75] M. Reuter and C. Wetterich, Running gauge coupling in three-dimensions and the electroweak phase transition, Nucl. Phys.B 408 (1993) 91 [SPIRES]. [76] K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3 − D physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis, Nucl. Phys.B 442 (1995) 317 [hep-lat/9412091] [SPIRES]. [77] K. Holland, Another weak first order deconfinement transition: three-dimensional SU(5) gauge theory, JHEP01 (2006) 023 [hep-lat/0509041] [SPIRES]. [78] P. de Forcrand and O. Jahn, Deconfinement transition in 2 + 1-dimensional SU(4) lattice gauge theory, Nucl. Phys. Proc. Suppl.129 (2004) 709 [hep-lat/0309153] [SPIRES]. [79] K. Holland, M. Pepe and U.-J. Wiese, Revisiting the deconfinement phase transition in SU(4) Yang-Mills theory in 2 + 1 dimensions, JHEP02 (2008) 041 [arXiv:0712.1216] [SPIRES]. [80] L. von Smekal, S.R. Edwards and N. Strodthoff, Universal aspects of deconfinement in 2 + 1 dimensions, AIP Conf. Proc.1343 (2011) 212 [arXiv:1012.1712] [SPIRES]. [81] J. Liddle and M. Teper, The deconfining phase transition in D = 2 + 1 SU(N) gauge theories, arXiv:0803.2128 [SPIRES]. [82] M. Creutz, Monte Carlo study of quantized SU(2) gauge theory, Phys. Rev.D 21 (1980) 2308 [SPIRES]. [83] A.D. Kennedy and B.J. Pendleton, Improved heat bath method for Monte Carlo calculations in lattice gauge theories, Phys. Lett.B 156 (1985) 393 [SPIRES]. [84] S.L. Adler, An overrelaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions, Phys. Rev.D 23 (1981) 2901 [SPIRES]. [85] F.R. Brown and T.J. Woch, Overrelaxed heat bath and metropolis algorithms for accelerating pure gauge Monte Carlo calculations, Phys. Rev. Lett.58 (1987) 2394 [SPIRES]. [86] N. Cabibbo and E. Marinari, A new method for updating SU(N) matrices in computer simulations of gauge theories, Phys. Lett.B 119 (1982) 387 [SPIRES]. [87] SciDAC collaboration, R.G. Edwards and B. Joó, The chroma software system for lattice QCD, Nucl. Phys. Proc. Suppl.140 (2005) 832 [hep-lat/0409003] [SPIRES]. [88] M. Caselle, M. Pepe and A. Rago, Static quark potential and effective string corrections in the (2 + 1)-d SU(2) Yang-Mills theory, JHEP10 (2004) 005 [hep-lat/0406008] [SPIRES]. [89] F. Gliozzi, The Stefan-Boltzmann law in a small box and the pressure deficit in hot SU(N) lattice gauge theory, J. Phys.A 40 (2007) F375 [hep-lat/0701020] [SPIRES]. [90] M. Panero, Geometric effects in lattice QCD thermodynamics, PoSLATTICE2008 (2008) 175 [arXiv:0808.1672] [SPIRES]. [91] T. Umeda et al., Fixed scale approach to equation of state in lattice QCD, Phys. Rev.D 79 (2009) 051501 [arXiv:0809.2842] [SPIRES]. [92] J. Engels, J. Fingberg, F. Karsch, D. Miller and M. Weber, Nonperturbative thermodynamics of SU(N) gauge theories, Phys. Lett.B 252 (1990) 625 [SPIRES]. [93] M. Caselle, M. Hasenbusch and M. Panero, The interface free energy: comparison of accurate Monte Carlo results for the 3D Ising model with effective interface models, JHEP09 (2007) 117 [arXiv:0707.0055] [SPIRES]. [94] G. Karl and J.E. Paton, Gluonic states in two space dimensions, Phys. Rev.D 61 (2000) 074002 [hep-ph/9910413] [SPIRES]. [95] G. Karl and J.E. Paton, Gluelump spectrum in the bag model, Phys. Rev.D 60 (1999) 034015 [hep-ph/9904407] [SPIRES]. [96] P. Bialas, L. Daniel, A. Morel and B. Petersson, Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture, Nucl. Phys.B 836 (2010) 91 [arXiv:0912.0206] [SPIRES]. · Zbl 1206.81094 [97] B. Zwiebach, A first course in string theory, Cambridge University Press, Cambridge U.K. (2004). · Zbl 1072.81001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.