# Lectures on Matrix Field Theory I

@article{Ydri2016LecturesOM, title={Lectures on Matrix Field Theory I}, author={Badis Ydri}, journal={arXiv: High Energy Physics - Theory}, year={2016} }

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.

## 21 Citations

### Approximate treatment of noncommutative curvature in quartic matrix model

- Physics
- 2022

: We study a Hermitian matrix model with the standard quartic potential amended by a tr( R Φ 2 ) term for ﬁxed external matrix R . This is motivated by a curvature term in the truncated Heisenberg…

### On the quantum structure of space-time, gravity, and higher spin in matrix models

- PhysicsClassical and Quantum Gravity
- 2020

In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by…

### Quantum gravity as a multitrace matrix model

- Mathematics
- 2017

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of…

### Fuzzy field theories and related matrix models

- Computer Science
- 2020

The multi-trace matrix models relevant for the analytical description of scalar field theories on fuzzy spaces are introduced and it is shown to what extent they do and do not, describe the know phase structure of $\phi^4$ theory on the fuzzy sphere.

### Detecting scaling in phase transitions on the truncated Heisenberg algebra

- Mathematics, Physics
- 2020

We construct and analyze the phase diagram of the self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. The model reduces to renormalizable…

### M ay 2 01 6 Equivariant Fields in an SU ( N ) Gauge theory with new Spontaneously Generated Fuzzy Extra Dimensions

- Physics
- 2018

We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of N = 4 supersymmetric Yang-Mills (SYM) theory with cubic soft supersymmetry breaking and mass…

### Equivariant Fields in an $SU({\cal N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions

- Physics
- 2015

We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of N = 4 supersymmetric Yang-Mills (SYM) theory with cubic soft supersymmetry breaking and mass…

### Equivariant Fields in an $SU({\cal N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions

- Physics
- 2016

We find new spontaneously generated fuzzy extra dimensions emerging from a certain deformation of $N=4$ supersymmetric Yang-Mills (SYM) theory with cubic soft supersymmetry breaking and mass…

### A U (3) Gauge Theory on Fuzzy Extra Dimensions

- Physics
- 2018

In this article, we explore the low energy structure of a U (3) gauge theory over spaces with fuzzy sphere(s) as extra dimensions. In particular, we determine the equivariant parametrization of the…

### Second moment fuzzy-field-theory-like matrix models

- Computer ScienceJournal of High Energy Physics
- 2020

A multitrace matrix model approximating the real quartic scalar field theory on the fuzzy sphere is solved and a modification of the kinetic part of the action by higher derivative term can change the phase diagram of the theory such that the triple point moves further from the origin.

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