Beyond second-moment approximation in fuzzy-field-theory-like matrix models

TL;DR

This paper explores advanced multi-trace matrix models for fuzzy scalar field theories, incorporating higher moments to accurately replicate their complex phase structures, including phase transitions and critical points.

Contribution

It introduces a novel multi-trace matrix model considering up to the fourth moment, capturing the phase behavior of fuzzy field theories more precisely.

Findings

Reproduces the phase structure observed in numerical simulations.

Identifies the existence of a uniform order phase and a triple point.

Models the transition line between different phases accurately.

Abstract

We investigate the phase structure of a special class of multi-trace hermitian matrix models, which are candidates for the description of scalar field theory on fuzzy spaces. We include up to the fourth moment of the eigenvalue distribution into the multi-trace part of the probability distribution, which stems from the kinetic term of the field theory action. We show that by considering different multi-trace behavior in the large moment and in the small moment regimes of the model, it is possible to obtain a matrix model, which describes the numerically observed phase structure of fuzzy field theories. Including the existence of uniform order phase, triple point, and an approximately straight transition line between the uniform and non-uniform order phases.