Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb C P^n$

TL;DR

This paper analyzes the phase diagram of scalar field theory on fuzzy complex projective spaces, identifying uniform, disorder, and non-uniform phases, and locating the triple point through perturbative and non-perturbative methods.

Contribution

It introduces a non-perturbative approximation for the effective action of scalar fields on fuzzy $ ext{CP}^n$, revealing new phase structures and phase boundaries.

Findings

Existence of a uniform order phase in the model.

Identification of phase boundaries and the triple point.

Agreement with previous numerical results for fuzzy sphere case.

Abstract

We study the phase structure of the scalar field theory on fuzzy $\mathbb C P^n$ in the large $N$ limit. Considering the theory as a hermitian matrix model we compute the perturbative expansion of the kinetic term effective action under the assumption of distributions being close to the semicircle. We show that this model admits also a uniform order phase, corresponding to the asymmetric one-cut distribution, and we find the phase boundary. We compute a non-perturbative approximation to the effective action which enables us to identify the disorder and the non-uniform order phases and the phase transition between them. We locate the triple point of the theory and find an agreement with previous numerical studies for the case of the fuzzy sphere.