Gross-Witten-Wadia transition in a matrix model of deconfinement

Abstract

We study the deconfining phase transition at nonzero temperature in a SU(N) gauge theory, using a matrix model which was analyzed previously at small N. We show that the model is soluble at infinite N, and exhibits a Gross-Witten-Wadia transition. In some ways, the deconfining phase transition is of first order: at a temperature $T_d$, the Polyakov loop jumps discontinuously from 0 to1/2, and there is a nonzero latent heat $\sim N^2$. In other ways, the transition is of second order: e.g., the specific heat diverges as $C\sim 1/(T-T_d{)}^{3/5}$ when $T\to T_d^{+}$. Other critical exponents satisfy the usual scaling relations of a second order phase transition. In the presence of a nonzero background field $h$ for the Polyakov loop, there is a phase transition at the temperature $T_h$ where the value of the loop =1/2, with $T_h<T_d$. Since $\partial C/\partial T\sim 1/(T-T_h{)}^{1/2}$ as $T\to T_h^{+}$, this transition is of third order.

7pages, 1 figure; discussion on matrix models is extended; references are added

References in corpus (11)

• Effective Theory of Wilson Lines and Deconfinement
• QCD Thermodynamics from the Lattice
• How Wide is the Transition to Deconfinement?
• Suppression of the Shear Viscosity in a "semi" Quark Gluon Plasma
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• Continuum Thermodynamics of the GluoN_c Plasma
• Critical endpoint for deconfinement in matrix and other effective models
• Polyakov Loop and Gluon Quasiparticles in Yang-Mills Thermodynamics
• Finite Volume Phases of Large N Gauge Theories with Massive Adjoint Fermions
• Zero Point Energy of Renormalized Wilson Loops
• Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory

Cited by in corpus (16)

• Polyakov loop modeling for hot QCD
• Production and Elliptic Flow of Dileptons and Photons in the semi-Quark Gluon Plasma
• Effective matrix model for deconfinement in pure gauge theories
• Chiral matrix model of the semi-Quark Gluon Plasma in QCD
• Collisional energy loss above the critical temperature in QCD
• The Roberge-Weiss transition and 't Hooft loops
• 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
• Zero interface tension at the deconfining phase transition for a matrix model of a $SU(\infty )$ gauge theory
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• Real-time hard-thermal-loop gluon self-energy in a semiquark-gluon plasma
• The Polyakov loop models in the large N limit: Phase diagram at finite density
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• Wilson loops in the Hamiltonian formalism