Matrix Models for Deconfinement and Their Perturbative Corrections

Abstract

Matrix models for the deconfining phase transition in $SU(N)$ gauge theories have been developed in recent years. With a few parameters, these models are able to reproduce the lattice results of the thermodynamic quantities in the semi-quark gluon plasma(QGP) region. They are also used to compute the behavior of the 't Hooft loop and study the exceptional group $G(2)$. In this paper, we review the basic ideas of the construction of these models and propose a new form of the non-ideal corrections in the matrix model. In the semi-QGP region, our new model is in good agreement with the lattice simulations as the previous ones, while in higher temperature region, it reproduces the upward trend of the rescaled trace anomaly as found in lattice which, however, can not be obtained from the previous models. In addition, we discuss the perturbative corrections to the thermal effective potential which could be used to systematically improve the matrix models at high temperatures. In particular, we provide, for the first time, an analytical proof of the relation between the one- and two-loop effective potential: two-loop correction is proportional to the one-loop result, independent of the eigenvalues of the Polyakov loop. This is a very general result, we prove it for all classic groups, including $SU(N)$, $SO(2N+1)$, $SO(2N)$ and $Sp(2N)$.

29 pages, 1 table, 5 figs, final version to appear in JHEP

References in corpus (7)

• Thermodynamics of the QCD plasma and the large-N limit
• Precision SU(3) lattice thermodynamics for a large temperature range
• Z(N) interface tension in a hot SU(N) gauge theory
• Gluon Quasiparticles and the Polyakov Loop
• Constrained effective potential in hot QCD
• Trace Anomaly and Quasi-Particles in Finite Temperature SU(N) Gauge Theory
• Spatial 't Hooft loop to cubic order in hot QCD

Cited by in corpus (13)

• Exceptional thermodynamics: The equation of state of G(2) gauge theory
• Two-loop perturbative corrections to the constrained effective potential in thermal QCD
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Effective models of a semi-quark gluon plasma
• Free energy of a Holonomous Plasma
• Collisional energy loss of a heavy quark in a semiquark-gluon plasma
• Resummed Gluon Propagator and Debye Screening Effect in a Holonomous Plasma
• Effective Debye Screening Mass in an Anisotropic Quark Gluon Plasma
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• Wilson loops in the Hamiltonian formalism
• Influence of a nontrivial Polyakov loop on the quarkonium states
• Suppression of the jet quenching parameter near the critical temperature
• Energy Loss of a Heavy Quark in a Collisional Quark-Gluon Plasma