Review of Matrix Theory

Abstract

In this article we present a self contained review of the principles of Matrix Theory including the basics of light cone quantization, the formulation of 11 dimensional M-Theory in terms of supersymmetric quantum mechanics, the origin of membranes and the rules of compactification on 1,2 and 3 tori. We emphasize the unusual origins of space time and gravitation which are very different than in conventional approaches to quantum gravity. Finally we discuss application of Matrix Theory to the quantum mechanics of Schwarzschild black holes. This work is based on lectures given by the second author at the Cargese ASI 1997 and at the Institute for Advanced Study in Princeton.

45 pages, LaTeX, 2 figures in .eps format

References in corpus (2)

• The World as a Hologram
• The Incredible Shrinking Torus

Cited by in corpus (42)

• The holographic principle
• U-duality and M-Theory
• Noncommutative Geometry From Strings and Branes
• Introduction to M(atrix) theory and noncommutative geometry
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• A Matrix Big Bang
• Emergent Gravity from Noncommutative Gauge Theory
• Linearized supergravity from Matrix theory
• On the Differential Geometry of $G{L}_q(1|1)$
• Supergravity currents and linearized interactions for Matrix Theory configurations with fermionic backgrounds
• Time-dependent AdS/CFT Duality and Null Singularity
• Modular Wedge Localization and the d=1+1 Formfactor Program
• Strings, loops and others: a critical survey of the present approaches to quantum gravity
• Non-Standard neutral kaons dynamics from D-brane statistics
• Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk Metric and Possible Resolution of Singularity
• ((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory
• Holomorphic curves from matrices
• Light-Front-Quantized QCD in Covariant Gauge
• Matrix Theory on ALE Spaces and Wrapped Membranes
• Non-perturbative states in type II superstring theory from classical spinning membranes
• Matrix Theory in a Constant C Field Background
• World Volume Noncommutativity versus Target Space Noncommutativity
• Conservation of Supergravity Currents from Matrix Theory
• Matrix string theory, contact terms, and superstring field theory
• Fields, Strings, Matrices and Symmetric Products
• A perturbative expansion scheme for supermembrane and matrix theory
• Large N and the Dine-Rajaraman problem
• Matrix Representations of Holomorphic Curves on $T_4$
• Renormalization of Higher Derivative Operators in the Matrix Model
• Stringy Membranes in AdS/CFT
• D0-branes in an H-field Background and Noncommutative Geometry
• 0-brane Quantum Chemistry
• Matrix Theory for the DLCQ of Type IIB String Theory on the AdS/Plane-wave
• A Note on Six-Dimensional Gauge Theories
• Quiver Matrix Mechanics for IIB String Theory (II): Generic Dual Tori, Fractional Matrix Membrane and $SL(2,\integer)$ Duality
• Feynman Graphs from D-Particle Dynamics
• Noncommutativities of D-branes and $\theta$-changing Degrees of Freedom in D-brane Matrix Models
• Energy spectrum and wave-functions of four-dimensional Supersymmetric Yang-Mills Quantum Mechanics for very high cut-offs
• Hidden Symmetries of M Theory
• An alternative way to explain how non-commutativity arises in the bosonic string theory
• Ward Identity for Membranes
• The Principle of Equivalence as a Guide towards Matrix Theory Compactifications