Effective matrix model for deconfinement in pure gauge theories

Abstract

We construct matrix models for the deconfining phase transition in SU(N) gauge theories, without dynamical quarks, at a nonzero temperature T. We generalize models with zero and one free parameter to study a model with two free parameters: besides perturbative terms ~T^4, we introduce terms ~T^2 and ~T^0. The two N-dependent parameters are determined by fitting to data from numerical simulations on the lattice for the pressure, including the latent heat. Good agreement is found for the pressure in the semi-quark gluon plasma (QGP), which is the region from Tc, the critical temperature, to about ~4 Tc. Above ~1.2 Tc, the pressure is a sum of a perturbative term, ~ +T^4, and a simple non-perturbative term, essentially just a constant times ~ -Tc^2 T^2. For the pressure, the details of the matrix model only enter within a very narrow window, from Tc to ~1.2 Tc, whose width does not change significantly with N. Without further adjustment, the model also agrees well with lattice data for the 't Hooft loop. This is notable, because in contrast to the pressure, the 't Hooft loop is sensitive to the details of the matrix model over the entire semi-QGP. For the (renormalized) Polyakov loop, though, our results disagree sharply with those from the lattice. Matrix models provide a natural and generic explanation for why the deconfining phase transition in SU(N) gauge theories is of first order not just for three, but also for four or more colors. Lastly, we consider gauge theories where there is no strict order parameter for deconfinement, such as for a G(2) gauge group. To agree with lattice measurements, in the G(2) matrix model it is essential to add terms which generate complete eigenvalue repulsion in the confining phase.

80 pages, 26 figures

References in corpus (39)

• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Strongly coupled plasma with electric and magnetic charges
• Renormalized Polyakov loops in many representations
• Angular Dependence of Jet Quenching Indicates Its Strong Enhancement Near the QCD Phase Transition
• Dynamical quasiparticles properties and effective interactions in the sQGP
• Effective Theory of Wilson Lines and Deconfinement
• Exceptional Deconfinement in G(2) Gauge Theory
• QCD Thermodynamics from the Lattice
• QCD thermodynamics and confinement from a dynamical quasiparticle point of view
• Magnetic Component of Quark-Gluon Plasma is also a Liquid!
• On the Nature of the Phase Transition in SU(N), Sp(2) and E(7) Yang-Mills theory
• Confining ensemble of dyons
• Color Screening, Casimir Scaling, and Domain Structure in G(2) and SU(N) Gauge Theories
• How Wide is the Transition to Deconfinement?
• Suppression of the Shear Viscosity in a "semi" Quark Gluon Plasma
• Fixed Scale Approach to Equation of State in Lattice QCD
• Continuum Thermodynamics of the GluoN_c Plasma
• Some Thermodynamic Aspects of Pure Glue, Fuzzy Bags and Gauge/String Duality
• Critical endpoint for deconfinement in matrix and other effective models
• Z(3)-symmetric effective theory for SU(3) Yang-Mills theory at high temperature
• G_2 gauge theory at finite temperature
• Renormalized Polyakov Loop in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions I - The confining phase
• Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics
• Center-Symmetric Effective Theory for High-Temperature SU(2) Yang-Mills Theory
• Extensions and further applications of the nonlocal Polyakov--Nambu--Jona-Lasinio model
• Casimir Scaling and String Breaking in G(2) Gluodynamics
• On Yang-Mills Theories with Chiral Matter at Strong Coupling
• Width of the QCD transition in a Polyakov-loop DSE model
• Zero Point Energy of Renormalized Wilson Loops
• The Spatial String Tension in the Deconfined Phase of SU(N) Gauge Theory and Gauge/String Duality
• Phase diagram of the lattice G(2) Higgs Model
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• Confinement and deconfinement for any gauge group from dyons viewpoint
• Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
• Modified Bag Models for the Quark Gluon Plasma Equation of State
• Magnetic monopole loops generated from two-instanton solutions: Jackiw-Nohl-Rebbi versus 't Hooft instanton
• Confinement, Screening and the Center on S^3 x S^1

Cited by in corpus (68)

• Improved Polyakov-loop potential for effective models from functional calculations
• Production and Elliptic Flow of Dileptons and Photons in the semi-Quark Gluon Plasma
• Non-Abelian Dark Forces and the Relic Densities of Dark Glueballs
• Phase diagram and surface tension in the three-flavor Polyakov-quark-meson model
• Non-perturbative finite-temperature Yang-Mills theory
• Gluon screening mass at finite temperature from Landau gauge gluon propagator in lattice QCD
• The Present and Future of QCD
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Two-loop study of the deconfinement transition in Yang-Mills theories: SU(3) and beyond
• Gravitational Waves from Dark Yang-Mills Sectors
• Dark Confinement and Chiral Phase Transitions: Gravitational Waves vs Matter Representations
• QCD thermodynamics from lattice calculations with non-equilibrium methods: The SU(3) equation of state
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Introductory lectures to large-N QCD phenomenology and lattice results
• Polyakov loop and QCD thermodynamics from the gluon and ghost propagators
• Dark Confinement-Deconfinement Phase Transition: A Roadmap from Polyakov Loop Models to Gravitational Waves
• Debye screening mass near deconfinement from holography
• Yang-Mills correlators across the deconfinement phase transition
• Chiral spin symmetry and the QCD phase diagram
• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Two-loop perturbative corrections to the thermal effective potential in gluodynamics
• Effective potential for SU(2) Polyakov loops and Wilson loop eigenvalues
• Modeling the nonperturbative contributions to the complex heavy-quark potential
• Phase diagram and nucleation in the Polyakov-loop-extended Quark-Meson truncation of QCD with the unquenched Polyakov-loop potential
• Thermodynamics and phase diagrams of Polyakov-loop extended chiral models
• A novel background field approach to the confinement-deconfinement transition
• Two-loop perturbative corrections to the constrained effective potential in thermal QCD
• Effective Polyakov line action from the relative weights method
• The Roberge-Weiss transition and 't Hooft loops
• Polyakov loop and gluon quasiparticles: a self-consistent approach to Yang-Mills thermodynamics
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Covariant variational approach to Yang-Mills Theory: effective potential of the Polyakov loop
• Effective models of a semi-quark gluon plasma
• Free energy of a Holonomous Plasma
• Glueballs and the Yang-Mills plasma in a $T$-matrix approach
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory
• Fluctuations of order parameter in an $SU(N_c)$ effective model
• The fate of the critical endpoint at large $N_c$
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Collisional energy loss of a heavy quark in a semiquark-gluon plasma
• Resummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• Thermodynamics of the Quark-Gluon Plasma in Terms of Quasiparticles and Polyakov Line Condensates
• Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
• Perturbative aspects of the deconfinement transition -- Physics beyond the Faddeev-Popov model
• Implementation of chromomagnetic gluons in Yang-Mills thermodynamics
• Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma
• Thermodynamic inconsistency in quasiparticle model - a revisit
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• Conserved Charge Fluctuations and Susceptibilities in Strongly Interacting Matter
• Deconfinement in the presence of a strong magnetic field
• Probing confinement by direct photons and dileptons
• A window on infrared QCD with small expansion parameters
• Wilson loops in the Hamiltonian formalism
• Hydrodynamics of a quark droplet II: Implications of a non-zero baryon chemical potential
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• Anisotropy of thermal dileptons
• Influence of a nontrivial Polyakov loop on the quarkonium states
• The SUSY Yang-Mills plasma in a $T$-matrix approach
• Deconfinement on ${\mathbb{R}}^2\times S_L^1\times S_{\beta }^1$ for all gauge groups and duality to double Coulomb Gas
• The effective potential of the Polyakov loop in the Hamiltonian approach to QCD
• Massive Gauge Theory with Quasigluon for Hot $SU(N)$: Phase Transition and Thermodynamics
• Novel first-order phase transition and critical points in SU(3) Yang-Mills theory with spatial compactification
• Suppression of the jet quenching parameter near the critical temperature
• Interplay between chromoelectric and chromomagnetic gluons in Yang-Mills thermodynamics
• Effective Matrix Model for Gauge Theories at Finite Temperature and Density using Quantum Computing
• Energy Loss of a Heavy Quark in a Collisional Quark-Gluon Plasma