The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CPⁿ

Abstract

We perform a high-temperature expansion of scalar quantum field theory on fuzzy CPⁿ 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 CP¹.