Deconfinement in matrix models about the Gross-Witten point

Abstract

We study the deconfining phase transition in SU (N ) gauge theories at nonzero temperature using a matrix model of Polyakov loops. The most general effective action, including all terms up to two spatial derivatives, is presented. At large N , the action is dominated by the loop potential: following Aharony et al., we show how the Gross-Witten model represents an ultra-critical point in this potential. Although masses vanish at the Gross-Witten point, the transition is of first order, as the fundamental loop jumps only halfway to its perturbative value. Comparing numerical analysis of the N = 3 matrix model to lattice simulations, for three colors the deconfining transition appears to be near the Gross-Witten point. To see if this persists for N ≥ 4, we suggest measuring within a window ∼ 1/N 2 of the transition temperature.

Phases ofN=∞QCD-like gauge theories onS3×S1and nonperturbative orbifold-orientifold equivalences

“…In this sense, the quantum theories in the N = ∞ limit behave as classical [57]. 23 The difference in the loop equations of QCD(AS/S) and QCD(BF) and QCD(adj) essentially arises in these subleading terms. Such fluctuations are typically of O(1/N ) for QCD(AS/S) and O(1/N 2 ) for QCD(BF/adj).…”

“…The loop equations of operators in these subsectors are unrelated to one another, and there is no map between them. 23 The clustering property breaks down if the theory is in the mixed phase (or there are more than one vacuum) in the theory. All of our n f = 1 QCD-like theories, SYM, QCD(AS/S/BF) has N isolated vacua (in leading order in large N ) characterised by their chiral condensate in R 4 .…”

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

“…As a function of temperature, it exhibits a GrossWitten-Wadia transition [17]. That is, it exhibits aspects of both first order and second order phase transitions; thus it can be termed "critical first order" [12]. Since the theory has finite spatial volume, however, there is only a true phase transition at infinite N .…”

“…Large N can be studied through numerical simulations [2] and in reduced models [3]. In the pure glue theory, this transition can be modeled through an effective model, such as a matrix model [4][5][6][7][8][9][10].One limit in which the theory can be solved analytically is by putting it on a sphere of femto-scale dimensions [11,12]. An effective theory is constructed directly by integrating out all modes with nonzero momentum, and gives a matrix model which is soluble at large N [13][14][15][16].…”

“…One limit in which the theory can be solved analytically is by putting it on a sphere of femto-scale dimensions [11,12]. An effective theory is constructed directly by integrating out all modes with nonzero momentum, and gives a matrix model which is soluble at large N [13][14][15][16].…”