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

TL;DR

This paper derives a multitrace matrix model for scalar field theory on fuzzy complex projective spaces, analyzes its phase diagram, and confirms previous numerical results for CP^1 using analytical methods.

Contribution

It introduces a high-temperature expansion and a multitrace matrix model approach for fuzzy CP^n, providing analytical insights into the phase structure.

Findings

Phase diagram analyzed for various n

Confirmation of previous numerical results for CP^1

Analytical saddle point evaluation of the partition function

Abstract

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