Quark-Gluon Plasma in Strong Magnetic Fields
Total Page：16
File Type：pdf, Size：1020Kb
Quark-gluon plasma in strong magnetic fields Dissertation zur Erlangung des Doktorgrades des Fachsbereichs Physik der Universit¨at Hamburg vorgelegt von Tigran Kalaydzhyan aus Jerewan Hamburg 2013 Gutachter der Dissertation: Prof. Dr. Volker Schomerus Dr. Ingo Kirsch Prof. Dr. Gerrit Schierholz Gutachter der Disputation: Prof. Dr. Jan Louis Dr. Ingo Kirsch Datum der Disputation: 10. April 2013 Vorsitzender des Pr¨ufungsausschusses: Prof. Dr. Bernd Kniehl Vorsitzender des Promotionsausschusses: Prof. Dr. Peter Hauschildt Dekan der Fakult¨at f¨ur Mathematik, Informatik und Naturwissenschaften: Prof. Dr. Heinrich Graener Abstract One of the fundamental problems in subatomic physics is the determination of properties of matter at extreme temperatures, densities and electromagnetic fields. The modern ultrarelativistic heavy- ion experiments are able to study such states (the quark-gluon plasma) and indicate that the physics at extreme conditions differs drastically from what is known from the conventional observations. Also the theoretical methods developed mostly within the perturbative framework face various conceptual problems and need to be replaced by a nonperturbative approach. In this thesis we study the physics of the strongly-coupled quark-gluon plasma in external magnetic fields as well as general electromagnetic and topological properties of the QCD and QCD-like systems. We develop and apply various nonperturbative techniques, based on e.g. gauge-gravity correspondence, lattice QCD simulations, relativistic hydrodynamics and condensed-matter-inspired models. The thesis is mainly based on our papers [1–15], with corrections and additional comments. Zusammenfassung Eines der fundamentalen Probleme subatomarer Physik ist die Bestimmung der Eigenschaften von Materie bei extremen Temperaturen, Dichten und elektromagnetischen Feldern. Moderne Exper- imente mit ultrarelativistischen Schwerionen sind in der Lage Zust¨ande, wie das Quark-Gluon Plasma, unter diesen Verh¨altnissen zu untersuchen und zeigen, dass sich die Physik unter solch extremen Bedingungen drastisch vom Verhalten unter gew¨ohnlichen Bedingungen unterscheidet. Weiterhin sind theoretische Modelle, die auf St¨orungstheorie basieren, unter solchen Umst¨anden nicht anwendbar und m¨ussen durch nichtperturbative Methoden ersetzt werden. In dieser Ar- beit untersuchen wir daher die Physik des stark gekoppelten Quark-Gluon Plasmas in externen magnetischen Feldern sowie elektromagnetische und topologische Eigenschaften von QCD und QCD-¨ahnlichen Systemen. Hierzu entwickeln und verwenden wir verschiedene nichtperturbative Methoden, die unter anderem auf der Gauge-Gravity-Korrespondenz, Gitter-QCD Simulationen, relativistischer Hydrodynamik und Festk¨orper-inspirierten Modellen basieren. Diese Arbeit basiert auf unseren Ver¨offentlichungen [1–15] und enth¨alt Korrekturen sowie zus¨atzliche Kommentare. Contents 1 Introduction and overview 7 2 Gauge-gravity duality 13 3 Non-equilibrium physics at a holographic chiral phase transition 18 3.1 HolographicDescriptions. ........ 21 3.1.1 Chiralsymmetrytransition . ..... 21 3.1.2 Aboost-invariantexpandingplasma . ....... 23 3.2 Out of equilibrium description of the chiral phase transition............. 25 3.2.1 D7flavourbraneaction . .. .. .. .. .. .. .. .. .. .. .. .. 26 3.2.2 Naive equilibrium based approximation . ........ 27 3.2.3 Adiabatic dynamic D7 brane embeddings . ...... 28 3.2.4 FullPDEsolutions.............................. .. 30 3.3 Dependence of the condensate on B .......................... 34 3.4 Discussion...................................... ... 36 4 Holographic dual of a boost-invariant plasma with chemical potential 38 4.1 Late-time background in Eddington-Finkelstein coordinates ............. 39 4.1.1 Boostedblackbranesolution . ..... 39 4.1.2 Zeroth-order solution and first-order correction . ............. 40 4.1.3 Transport coefficients from the background . ........ 42 4.2 Late-time solution in Fefferman-Graham coordinates . .............. 44 4.2.1 General ansatz and near-boundary behaviour . ......... 44 4.2.2 Late-timeansatzforthebackground . ....... 45 4.2.3 Zeroth-ordersolution. ..... 47 4.2.4 Fefferman-Graham vs. Eddington-Finkelstein coordinates .......... 51 4.3 Conclusions ..................................... ... 52 5 Fluid-gravity model for the chiral magnetic effect 55 5.1 CMEandCVEinhydrodynamics . ... 56 5.2 Fluid-gravitymodelfortheCME . ....... 58 6 Anisotropic hydrodynamics, holography and the chiral magneticeffect 64 6.1 Hydrodynamics of anisotropic fluids with triangle anomalies............. 65 6.1.1 Thermodynamics of an anisotropic fluid with chemical potential (n =1).. 66 6.1.2 Vortical and magnetic coefficients (n =1)................... 67 6.1.3 Multiple charge case n arbitrary)........................ 68 6.1.4 Chiral magnetic and vortical effect (n =2) .................. 69 6.2 Fluid-gravitymodel .............................. ..... 71 6.2.1 AdS black hole with multiple U(1) charges . ....... 71 5 CONTENTS 6.2.2 Anisotropic AdS geometry with multiple U(1) charges . ........... 72 6.3 Holographic vortical and magnetic conductivities . ............... 75 6.3.1 First-ordercorrectedbackground . ........ 75 6.3.2 Holographicconductivities. ....... 76 6.3.3 Subtleties in holographic descriptions of the CME . ........... 78 6.4 Conclusions ..................................... ... 78 7 Quantum Chromodynamics on a Lattice 84 7.1 Improvedaction .................................. ... 84 7.2 Monte-Carloalgorithms . ...... 88 7.3 Overlapfermions ................................. .... 92 8 SU(3) quenched lattice gauge theory in magnetic fields 94 8.1 Technicaldetails ................................ ..... 94 8.2 Chiralcondensate................................ ..... 95 8.3 Chiral magnetization and susceptibility . ............ 96 8.4 Electricdipolemoment. ...... 98 8.5 Some evidences of the chiralmagnetic effect . ........... 98 9 Magnetic-Field-Induced insulator-conductor transition 100 10 Fractal dimension of the topological charge distribution 105 10.1 Technicaldetails ............................... ...... 106 10.1.1 OrdinaryIPRforzeromodes.. ..... 107 10.1.2 Chiral IPR for low-lying modes. First definition. ............ 107 10.1.3 Chiral IPR for zero modes. Second definition. .......... 108 10.1.4 Fractal dimension. Results and conclusions. ............ 108 11 Chiral superfluidity of the quark-gluon plasma 111 11.1 DerivationoftheeffectiveLagrangian . ........... 113 11.1.1 Thefunctionalintegral. ...... 113 11.1.2 Vectorcurrentsconservation . ....... 114 11.1.3 Anomalyfortheaxialcurrent. ...... 114 11.1.4 AxionicLagrangian . ... 116 11.1.5 InterpretationofΛ . .... 117 11.1.6 Fermionicspectrumandchirality . ........ 119 11.2 Quark-gluon plasma as a two-component fluid . ........... 120 11.2.1 Hydrodynamicequations . .... 121 11.2.2 Phenomenological output, possible tests of the model ............ 123 11.2.3 Change in entropy and higher order gradient corrections........... 123 11.2.4 PreliminaryestimatesfortheCME. ....... 125 11.3Conclusion ..................................... ... 127 12 On chromoelectric superconductivity of the Yang-Mills vacuum 128 13 Conclusions and Outlook 133 6 Chapter 1 Introduction and overview The modern nuclear experiments at the Relativistic Heavy Ion Collider (RHIC, BNL) and the Large Hadron Collider (LHC, CERN) provide us with the possibility to explore new high-energy forms of matter, such as the so-called quark-gluon plasma (QGP), which can be produced in ultrarelativistic heavy-ion collisions and consists of interacting quarks and gluons out of nucleons and mesons [16–18]. Each of the collision events begins from an intense heating in the volume occupied by the overlap of the nuclei, as a large fraction of their kinetic energy is converted into a high-temperature system of quarks, antiquarks and gluons. The time between the first contact of the nuclei and the formation of QGP is called τf , the formation time. The temperature of QGP is estimated to be more extreme as any of the known examples in the present universe and exceeds the critical temperature Tc 170 MeV of the deconfinement transition. In Ref. [19] assuming the formation time τ = 0.2∼ fm/c the initial temperatures are estimated to be T 330MeV for f 0 ∼ √s = 200 GeV per nucleon pair central Au-Au collisions at RHIC T0 610MeV for √s =2.76 TeV central Pb-Pb collisions at LHC1. Suppression of Υ(1S) mesons in √∼s =2.76 TeV Pb-Pb collisions [21,22] according to the quarkonia thermometry [23] leads to the conclusion that the temperatures T > 2 Tc have been indeed reached at LHC. At the next stage, the system, presumably a liquid of quarks and gluons, immediately expands and cools down, passing through the critical temperature Tc at which QGP condenses into a gas of hadrons. As expansion continues, the system reaches the “freeze-out” density, at which the hadrons no longer interact with each other and stream into detectors. Typical time and temperature scales for the RHIC and LHC collisions are shown in Table 1.0.1. An important property extensively used in many of the phenomenological models of QGP (including our ones) is that the matter content of QGP interacts collectively and forms hydrody- namic flows. This idea goes back to the works of Landau [24] and Bjorken [25] and can be studied experimentally by the analysis of the particle distribution in the transverse (to beam) plane, ∞ dN 1 d2N E = 1+2 v cos[n(ϕ Ψ )] , (1.0.1) d3p 2π p dp dy n − RP T T n=1 ! X where E is the energy of the particle with momentum ~p and transfer momentum