A phase transition in commuting Gaussian multi-matrix models

Understand

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).