Fuzzy field theories and related matrix models

TL;DR

This paper reviews how scalar field theories on fuzzy spaces can be modeled using Hermitian random matrix models, highlighting their successes and limitations in describing phase structures.

Contribution

It introduces multi-trace matrix models for scalar fields on fuzzy spaces and evaluates their effectiveness in capturing phase structures of $\

Findings

Multi-trace matrix models can describe some phase structures of scalar fields on fuzzy spaces.

Limitations exist in fully capturing the phase structure of $\

contribution

Abstract

We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most important results for the scalar fields on such spaces. We then introduce the multi-trace matrix models relevant for the analytical description of scalar field theories on fuzzy spaces and show to what extent they do, and to what extent they do not, describe the know phase structure of $\phi^4$ theory on the fuzzy sphere.