A phase transition in commuting Gaussian multi-matrix models

Abstract

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 / λR, where λis the 't Hooft coupling).

10 pages, 1 figure, latex. v3 (with a new title) corrects the wrong assumption that the dominant phase in gauge theories on S^3 involves commuting matrices, and the wrong conclusion that these theories have high temperature phase transitions; we thank Shiraz Minwalla for pointing this out

References in corpus (8)

• A first order deconfinement transition in large N Yang-Mills theory on a small 3-sphere
• All loop BMN state energies from matrices
• AdS black holes and thermal Yang-Mills correlators
• Instabilities of the Small Black Hole: a view from N=4 SYM
• 5d Black Hole as Emergent Geometry of Weakly Interacting 4d Hot Yang-Mills Gas
• Two loop partition function for large N pure Yang-Mills theory on a small three-sphere
• Topology change in commuting saddles of thermal N=4 SYM theory
• Thermal N = 4 SYM theory as a 2D Coulomb gas

Cited by in corpus (5)

• Multi-matrix models and emergent geometry
• Giant magnon bound states from strongly coupled N=4 SYM
• Hedgehog black holes and the Polyakov loop at strong coupling
• On the Phase Structure of Commuting Matrix Models
• Topology change in commuting saddles of thermal N=4 SYM theory