The Confining Transition in the Bosonic BMN Matrix Model

Abstract

We study the confining/deconfining phase transition in the mass deformed Yang-Mills matrix model which is obtained by the dimensional reduction of the bosonic sector of the four-dimensional maximally supersymmetric Yang-Mills theory compactified on the three sphere, i.e. the bosonic BMN model. The $1/D$ (with $D$ the number of matrices) expansion suggests that the model may have two closely separated transitions. However, using a second order lattice formulation of the model we find that for the small value of the mass parameter, $\mu =2$, those two apparent critical temperatures merge at large $N$, leaving only a single weakly first-order phase transition, in agreement with recent numerical results for $\mu =0$ (the bosonic BFSS model).

arXiv comment17 pages and 7 figures; v2: typos fixed, references added, minor editing and comments on double Gaussian approximation

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Cited by in corpus (3)

• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• Thermofield Theory of Large $N$ Matrix Models
• Non-perturbative phase structure of the bosonic BMN matrix model