Exact fuzzy sphere thermodynamics in matrix quantum mechanics

Abstract

We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the critical point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In the high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.

22 pages, 14 figures, (v2) some typos corrected

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Cited by in corpus (18)

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• Smearing Effect in Plane-Wave Matrix Model
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• D-dependence of gap between critical temperatures in one-dimensional gauge theories
• Phase Transitions of a (Super) Quantum Mechanical Matrix Model with a Chemical Potential
• Probing Smearing Effect by Point-Like Graviton in Plane-Wave Matrix Model