On Space-Time Supersymmetry and String Duality in Nine Dimensions

Abstract

N = 2 extended space-time supersymmetry in nine dimensions implies that the BPS states corresponding to momentum and winding of either of the type-II superstrings compactified on S’ transform as inequivalent supermultiplets. This fact can be checked using world-sheet techniques, and provides the physical basis for the connection between IIA superstring theory compactified on a circle of radius R and IIB theory compactified on a circle of radius l/R. Aspects of the duality between M-theory compactified on T2 and IIB theory compactified on S’ follow from the structure of N = 2, D = 9 supergravity. The coupling of N = 2, D = 9 supergravity to the BPS states is also discussed. In compactifications of the bosonic string theory on a circle of radius R, target space duality relates the theory obtained at radius R (we use string units) to the theory compactified at radius l/R [l]. Both the spectrum and the interactions exhibit a symmetry under R 4 l/R combined with an interchange of momentum and winding states and a change of sign of the leftmoving oscillators. This symmetry relates large and small distances, so that R can be restricted to the interval [l, m) and the theory appears to have a smallest length set by the string scale. At R = 00 the theory decompactifies while at the self-dual point R = 1 the winding and momentum states acquire equal masses and gauge symmetry enhancement takes place. The heterotic string possesses the same kind of duality symmetry [2]. In the case of the type-II string theories, the situation is different. Duality is not a symmetry, but it is expected to interpolate in a continuous manner between two distinct ten dimensional Lorentz invariant asymptotic theories, viz. the IIA and IIB superstring theories [3,4].