Lectures on Matrix Field Theory I

TL;DR

This paper provides an in-depth overview of matrix field theory, emphasizing matrix formulations of noncommutative spaces, phase structures of noncommutative  theory, and an introduction to noncommutative gauge theories, with a focus on non-perturbative methods.

Contribution

It offers a comprehensive lecture-based treatment of matrix field theory, highlighting non-perturbative approaches and detailed phase structure analysis of noncommutative  theory.

Findings

Detailed phase diagram of noncommutative  theory

Matrix formulation of noncommutative and fuzzy spaces

Introduction to noncommutative gauge theories

Abstract

The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.