A phase transition in commuting Gaussian multi-matrix models

Details A phase transition in commuting Gaussian multi-matrix models A phase transition in commuting Gaussian multi-matrix models

2007-06-19

arxiv.org/abs/0706.2861v3

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, 1 figure, latex. v3 (with a new title) corrects the wrong assumption that the dominant phase in gauge theories on S^

Scientific paper

We analyze in detail a second order phase transition that occurs in large N Gaussian multi-matrix models in which the matrices are constrained to be commuting. The phase transition occurs as the relative masses of the matrices are varied, assuming that there are at least four matrices in the lowest mass level. We also discuss the phase structure of weakly coupled large N 3+1 dimensional gauge theories compactified on a three-sphere of radius R. We argue that these theories are well described at high temperatures (T >> 1/R) by a Gaussian multi-matrix model, and that they do not exhibit any phase transitions between the deconfinement scale (T ~ 1/R) and the scale where perturbation theory breaks down (T ~ 1 / \lambda R, where \lambda is the 't Hooft coupling).

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