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The multitrace matrix model of scalar field theory on fuzzy \(\mathbb {C}P^n\). (English) Zbl 1217.81140

Summary: We perform a high-temperature expansion of scalar quantum field theory on fuzzy \(\mathbb {C}P^n\) to third order in the inverse temperature. Using group theoretical methods, we rewrite the result as a multitrace matrix model. The partition function of this matrix model is evaluated via the saddle point method and the phase diagram is analyzed for various \(n\). Our results confirm the findings of a previous numerical study of this phase diagram for \(\mathbb {C}P^n\).

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T28 Thermal quantum field theory
82B30 Statistical thermodynamics
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