Deconfinement in Matrix Models about the Gross--Witten Point

Details Deconfinement in Matrix Models about the Gross--Witten Point Deconfinement in Matrix Models about the Gross--Witten Point

2004-10-21

arxiv.org/abs/hep-ph/0410294v2

Phys.Rev. D71 (2005) 074004

Physics

High Energy Physics

High Energy Physics - Phenomenology

22 pages, 7 figures; revtex4. A new Fig. 2 illustrates a strongly first order transition away from the GW point; discussion ad

Scientific paper

10.1103/PhysRevD.71.074004

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.

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