Review of Matrix Theory
Daniela Bigatti, Leonard Susskind
TL;DR
Matrix Theory offers a nonperturbative description of M-theory via discrete light-cone quantization and D0-brane quantum mechanics, showing how 11D gravitons, membranes, and 5-branes emerge from matrix degrees of freedom. It connects IIA string theory, dualities, and emergent spatial directions through the DLCQ limit and a 0+1D supersymmetric gauge dynamics, and it provides a framework to study black holes by mapping their thermodynamics to large-N super Yang–Mills behavior. The work highlights partial matches between matrix-model calculations and supergravity (e.g., two-body graviton scattering) and explores nonperturbative effects (instantons in Y-exchange), while acknowledging unresolved issues such as higher-loop corrections, zero modes, and the full Lorentz-invariant recovery in the large-N limit. Overall, the paper argues that Matrix Theory captures essential nonperturbative string/M-theory features, including a mechanism for emergent space and dualities, with concrete links to black hole physics and holographic-like thermodynamics.
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.