Anatomy of a Duality

The nature of M–theory on K3×I, where I is a line interval, is considered, with a view towards formulating a “matrix theory” representation of that situation. Various limits of this compactification of M–theory yield a number of well known N=1 six dimensional compactifications of the heterotic and type I string theories. Geometrical relations between these limits give rise to string/string dualities between some of these compactifications. At a special point in the moduli space of compactifications, this motivates a partial definition of the matrix theory representation of the M–theory on K3×I as the large N limit of a certain type IA orientifold model probed by a conglomerate of N D–branes. Such a definition in terms of D–branes and orientifold planes is suggestive, but necessarily incomplete, due to the low amount of superymmetry. It is proposed —following hints from the orientifold model— that the complete matrix theory representation of the K3×I compactified M– theory is given by the large N limit of a compactification —on a suitable “dual” surface— of the “little E8×E8 heterotic string” N=1 six dimensional quantum theory.