Matrix model approximations of fuzzy scalar field theories and their phase diagrams

TL;DR

This paper compares two matrix model approximations of fuzzy scalar field theories, showing that the nonperturbative approach qualitatively matches known phase diagrams, while the perturbative one does not.

Contribution

It introduces and analyzes two multitrace matrix model approximations for fuzzy scalar field theories, highlighting their differing abilities to replicate expected phase diagram features.

Findings

Nonperturbative approximation reproduces correct phase diagram features.

Perturbative approximation shows unexpected phase diagram features.

Qualitative agreement with previous numerical studies for the nonperturbative model.

Abstract

We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.