Lectures on Matrix Field Theory I

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 ${\varphi }^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.

293 pages, 10 figures. Several small parts of these lectures have already appeared in various preprints found on the arXiv. I have felt no need to reword my own expressions if I thought they conveyed the physics properly

References in corpus (23)

• Algebras of distributions suitable for phase-space quantum mechanics. I
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• Multi-matrix models and emergent geometry
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Deconfinement phase transition in N=4 super Yang-Mills theory on RxS^3 from supersymmetric matrix quantum mechanics
• Geometry in transition: A model of emergent geometry
• Massive super Yang-Mills quantum mechanics: classification and the relation to supermembrane
• Finite temperature phase transition of a single scalar field on a fuzzy sphere
• The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CP^n
• Phase diagrams of the multitrace quartic matrix models of noncommutative Φ^4
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• On the Phase Structure of Commuting Matrix Models
• Random matrix approach to scalar fields on fuzzy spaces
• The One-Plaquette Model Limit of NC Gauge Theory in 2D
• Emergent geometry from random multitrace matrix models
• New Scaling Limit for Fuzzy Spheres
• Random vector and matrix and vector theories: a renormalization group approach
• Quantum Equivalence of NC and YM Gauge Theories in 2 D and Matrix Theory
• Construction of Fuzzy Spaces and Their Applications to Matrix Models
• Wilson RG of Noncommutative ${\Phi }_4^4$
• Impact of Supersymmetry on Emergent Geometry in Yang-Mills Matrix Models

Cited by in corpus (15)

• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Second moment fuzzy-field-theory-like matrix models
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Fuzzy $C{P}^2$ Space-Times
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Dirac operators for matrix algebras converging to coadjoint orbits
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Chaotic Dynamics of the Mass Deformed ABJM Model
• Chaos from Massive Deformations of Yang-Mills Matrix Models
• Equivariant Fields in an $SU(\mathcal{N})$ Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
• A $U(3)$ Gauge Theory on Fuzzy Extra Dimensions
• Chaos in Matrix Gauge Theories with Massive Deformations