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

TL;DR

This paper reviews matrix theory as a fundamental, eleven-dimensional quantum gravity framework underlying M-theory, discussing its formulation, evidence, and relation to other models, emphasizing its potential to unify gravity and quantum physics.

Contribution

It provides a comprehensive, accessible review of matrix theory's development, its relation to M-theory, and insights into its formulation and implications for fundamental physics.

Findings

Matrix theory is a well-defined quantum theory reducing to supersymmetric gravity at low energies.

Higher-dimensional objects like branes emerge from nonabelian matrix structures.

The review discusses challenges in formulating matrix theory in general space-time backgrounds.

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.