TASI Lectures on Matrix Theory

Abstract

This is a summary of key issues in Matrix Theory and its compactifications. It is emphasized that Matrix Theory is a valid Discrete Light Cone Quantization of M Theory with at least 6 noncompact asymptotically flat dimensions and 16 or 32 Supersymmetry Charges. The background dependence of the quantum mechanics of M Theory, and the necessity of working in light cone frame in asymptotically flat spacetimes are explained in terms of the asymptotic density of states of the theory, which follows from the Bekenstein-Hawking entropy formula. In four noncompact dimensions one is led to expect a Hagedorn spectrum in light cone energy. This suggests the possible relevance of ``little string theories'' (LSTs) to the quantum description of four dimensional compactifications, because one can argue that their exact high energy spectrum has the Hagedorn form. Some space is therefore devoted to a discussion of the properties of LSTs, which were first discovered as the proper formulation of Matrix Theory on the five torus.

JHEP LaTeX, 47 pages

Cited by in corpus (27)

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• Introduction to M(atrix) theory and noncommutative geometry, Part II
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• Emergent Spacetime
• D-branes and K-theory in 2D topological field theory
• Time-dependent AdS/CFT Duality and Null Singularity
• Black hole entropy from non-perturbative gauge theory
• Probing black holes in non-perturbative gauge theory
• Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk Metric and Possible Resolution of Singularity
• Fuzzy Geometry via the Spinor Bundle, with Applications to Holographic Space-time and Matrix Theory
• Background independent condensed matter models for quantum gravity
• Hair-brane Ideas on the Horizon
• CPT and Other Symmetries in String/M Theory
• Supergravity, Supermembrane and M(atrix) model on PP-Waves
• A perturbative expansion scheme for supermembrane and matrix theory
• Domain structures in quantum graphity
• Matrix model and noncommutative Chern-Simons theory
• Black Holes and String Theory
• Matrix Theory for the DLCQ of Type IIB String Theory on the AdS/Plane-wave
• Non-Supersymmetric String Theory
• Duality Symmetry in Kaluza-Klein $n+D+d$ Dimensional Cosmological Model
• Light-Cone Quantization: Foundations and Applications
• Remark about string field for general configuration of N D-instantons
• Discrete Light-Cone Quantization in PP-Wave Background
• Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models