Fuzzy Scalar Field Theory as Matrix Quantum Mechanics

TL;DR

This paper investigates the phase structure of a scalar field theory on a fuzzy sphere, reformulating it as a matrix quantum mechanics model with multitrace approximations, enabling analysis of its phase diagram.

Contribution

It introduces a novel approach to study scalar field theories on fuzzy spaces by mapping them to matrix quantum mechanics with multitrace terms, facilitating phase diagram analysis.

Findings

Phase diagram of the fuzzy sphere scalar field theory characterized.

Matrix model approximations enable standard analysis techniques.

New insights into noncommutative geometry effects on field theory.

Abstract

We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix model deformed by terms involving fixed external matrices. These terms can be approximated by multitrace expressions using a group theoretical method developed recently. The resulting matrix model is accessible to the standard techniques of matrix quantum mechanics.