<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>M</mml:mi></mml:math>theory as a matrix model: A conjecture

TLDR

The paper proposes a precise equivalence between uncompactified 11‑dimensional M theory and the N=∞ limit of supersymmetric matrix quantum mechanics of D0 branes. The equivalence is realized via a supersymmetric matrix quantum mechanics model whose membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime. Evidence for the conjecture comes from multiple correspondences, including that the matrix model reproduces the Fock space of massless supergravity particles, matches their leading large‑distance interactions, realizes the holographic principle, and contains membrane excitations.

Abstract

We suggest and motivate a precise equivalence between uncompactified 11-dimensional $M$ theory and the $N=\ensuremath{\infty}$ limit of the supersymmetric matrix quantum mechanics describing $D0$ branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by $M$ theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.