The Multitrace Matrix Model of Scalar Field Theory on Fuzzy $\mathbb CP^n$

We perform a high-temperature expansion of scalar quantum field theory on fuzzy $\mathbb CP^n$ 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 $\mathbb CP^1$.