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Unformatted text preview: arXiv:hep-th/9710231 v2 24 Dec 1997 RU-97-76 Matrix Theory T. Banks 1 1 Department of Physics and Astronomy Rutgers University, Piscataway, NJ 08855-0849 [email protected] This is an expanded version of talks given by the author at the Trieste Spring School on Supergravity and Superstrings in April of 1997 and at the accompanying workshop. The manuscript is intended to be a mini-review of Matrix Theory. The motivations and some of the evidence for the theory are presented, as well as a clear statement of the current puzzles about compactification to low dimensions. September 1997 1. INTRODUCTION 1.1. M Theory M theory is a misnomer. It is not a theory, but rather a collection of facts and arguments which suggest the existence of a theory. The literature on the subject is even somewhat schizophrenic about the precise meaning of the term M theory. For some authors it represents another element in a long list of classical vacuum configurations of “the theory formerly known as String ”. For others it is the overarching ur theory itself. We will see that this dichotomy originates in a deep question about the nature of the theory, which we will discuss extensively, but not resolve definitively. In these lectures we will use the term M theory to describe the theory which underlies the various string perturbation expansions. We will characterize the eleven dimensional quantum theory whose low energy limit is supergravity (SUGRA) with phrases like “the eleven dimensional limit of M theory ”. M theory arose from a collection of arguments indicating that the strongly coupled limit of Type IIA superstring theory is described at low energies by eleven dimensional supergravity  . Briefly, and somewhat anachronistically, the argument hinges on the existence of D0 brane solitons of Type IIA string theory . These are pointlike (in the ten dimensional sense) , Bogolmonyi-Prasad-Sommerfield (BPS) states 1 , with mass 1 l S g S . If one makes the natural assumption that there is a threshold bound state of N D0 branes for any N , then one finds in the strong coupling limit a spectrum of low energy states coinciding with the spectrum of eleven dimensional supergravity 2 . The general properties of M theory are derived simply by exploiting this fact, together with the assumed existence of membranes and fivebranes of the eleven dimensional theory 3 , on various partially compactified eleven manifolds . At this point we can already see the origins of the dichotomic attitude to M theory which can be found in the literature. In local field theory, the behavior of a system 1 For a review of BPS states and extensive references, see the lectures of J. Louis in these proceedings....
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