Type-IIB-string-M-theory duality and longitudinal membranes in M(atrix) theory

In this paper we study duality properties of the M(atrix) theory compactified on a circle. We present evidence for the equivalence of this theory to the strong coupling limit of type-IIB string theory compactified on a circle. In the M(atrix) theory context, our evidence for this duality consists of showing the appearance (upon compactification) of a topological term recently discovered in the D-string action, identifying the BPS states of type-IIB strings in the spectrum and finding the remnant symmetry of SL(2,Z) and the associated t moduli. By this type-IIB-string-M-theory duality, a number of insights are gained into the physics of longitudinal membranes in the infinite momentum frame.