Asymmetric hermitian matrix models and fuzzy field theory

TL;DR

This paper investigates hermitian matrix models with asymmetric solutions, analyzing phase diagrams and transitions, and applies these insights to fuzzy scalar field theories, aligning theoretical predictions with numerical simulations.

Contribution

It introduces methods to analyze asymmetric hermitian matrix models and applies them to fuzzy sphere field theories, revealing phase structures and triple points.

Findings

Phase diagram with two phase transitions for asymmetric quartic potential

Identification of a triple point in fuzzy sphere scalar field theory

Good agreement between theoretical and numerical results

Abstract

We analyze two types of hermitian matrix models with asymmetric solutions. One type breaks the symmetry explicitly with an asymmetric quartic potential. We give the phase diagram of this model with two different phase transitions between the one cut and two cut solutions. The second type, describing real scalar field theory on fuzzy spaces, breaks the symmetry spontaneously with multitrace terms. We present two methods to study this model, one direct and one using a connection with the first type of models. We analyze the model for the fuzzy sphere and obtain a phase diagram with the location of the triple point in a good agreement with the most recent numerical simulations.