Finite-temperature phase transitions of third and higher order in gauge theories at large $N$

Abstract

We study phase transitions in $SU(\infty )$ gauge theories at nonzero temperature using matrix models. Our basic assumption is that the effective potential is dominated by double trace terms for the Polyakov loops. As a function of the various parameters, related to terms linear, quadratic, and quartic in the Polyakov loop, the phase diagram exhibits a universal structure. In a large region of this parameter space, there is a continuous phase transition whose order is larger than second. This is a generalization of the phase transition of Gross, Witten, and Wadia (GWW). Depending upon the detailed form of the matrix model, the eigenvalue density and the behavior of the specific heat near the transition differ drastically. We speculate that in the pure gauge theory, that although the deconfining transition is thermodynamically of first order, it can be nevertheless conformally symmetric at infinite $N$.

37 pages, 9 figures

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Cited by in corpus (8)

• Gravitational Waves from Dark Yang-Mills Sectors
• Partial Deconfinement
• Effective models of a semi-quark gluon plasma
• Free energy of a Holonomous Plasma
• The Polyakov loop models in the large N limit: Phase diagram at finite density
• Wilson loops in the Hamiltonian formalism
• Shear and bulk viscosity for a pure glue theory using an effective matrix model
• Possible higher order phase transition in large-$N$ gauge theory at finite temperature