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 ).

Conundrum for the free energy of a holonomous gluonic plasma at cubic order

“…The natural choice are Polyakov loops [11], which are the order parameters for the deconfining phase transition in a SU(N) gauge theory, without dynamical quarks. Denoting the sources which couple to Polyakov loops as h, to ∼ g 2 the free energy is smoothly behaved as the holonomy vanishes, h → 0 [12][13][14][15][16][17][18][19][20][21][22]. In this note we show that something unexpected happens to ∼ g 3 .…”

Exceptional thermodynamics: the equation of state of G2 gauge theory

“…In fact, numerical simulations of this Yang-Mills theory have already been going on for some years [74][75][76][77][78][79][80][81][82][83][84][85]. Besides numerical studies, these peculiar features of G 2 Yang-Mills theory have also triggered analytical interest [86][87][88][89][90][91][92][93][94][95][96][97].…”

“…[94] (see also ref. [97]): following an idea discussed in refs. [91,182,190,191], in this article the thermal behavior of the theory near T c is assumed to depend on a condensate for the Polyakov-line eigenvalues, and the effective action due to quantum fluctuations in the presence of this condensate is computed at two loops.…”

Two-loop perturbative corrections to the constrained effective potential in thermal QCD

“…Recently, matrix models for deconfinement have been proposed which, with a relatively simple form, reproduce the lattice results in the phase transition region very well [15][16][17][18]. They are also generalized to the QCD case by including quarks [19].…”

“…Another motivation of this work is to study the relation between the one-and two-loop effective potential. For pure gauge theories, two-loop correction is proportional to the oneloop result, independent on the eigenvalues of the Polyakov loop [18,24]. Therefore, the former takes a very simple form including only the periodic Bernoulli polynomial B 4 (x).…”