M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory

TL;DR

This work reviews matrix theory as a fundamental description of M-theory in flat space, formulating it as a matrix quantum mechanics that regularizes the supermembrane and yields a nonperturbative, light-front definition of M-theory in the large-$N$ limit. It clarifies two equivalent pictures: a membrane-regularized matrix model and a DLCQ formulation of M-theory with D0-branes, showing how classical 11D gravity arises from quantum effects and how extended objects emerge from noncommuting matrices. The article develops the matrix regularization, analyzes how branes and interactions are encoded in matrix degrees of freedom, and discusses extensions to general backgrounds and connections to related models, while noting unresolved issues like background independence. Overall, it argues that matrix theory provides a calculational framework for quantum gravity across various regimes, tying together membranes, D-branes, and gravitational dynamics in a single, well-defined quantum system.

Abstract

A self-contained review is given of the matrix model of M-theory. The introductory part of the review is intended to be accessible to the general reader. M-theory is an eleven-dimensional quantum theory of gravity which is believed to underlie all superstring theories. This is the only candidate at present for a theory of fundamental physics which reconciles gravity and quantum field theory in a potentially realistic fashion. Evidence for the existence of M-theory is still only circumstantial---no complete background-independent formulation of the theory yet exists. Matrix theory was first developed as a regularized theory of a supersymmetric quantum membrane. More recently, the theory appeared in a different guise as the discrete light-cone quantization of M-theory in flat space. These two approaches to matrix theory are described in detail and compared. It is shown that matrix theory is a well-defined quantum theory which reduces to a supersymmetric theory of gravity at low energies. Although the fundamental degrees of freedom of matrix theory are essentially pointlike, it is shown that higher-dimensional fluctuating objects (branes) arise through the nonabelian structure of the matrix degrees of freedom. The problem of formulating matrix theory in a general space-time background is discussed, and the connections between matrix theory and other related models are reviewed.