Type I' and Real Algebraic Geometry

Abstract

We revisit the duality between type I' and heterotic strings in 9 dimensions. We resolve a puzzle about the validity of type I' perturbation theory and show that there are regions in moduli which are not within the reach of type I' perturbation theory. We find however, that all regions of moduli are described by a special class of real elliptic $K3$'s in the limit where the $K3$ shrinks to a one dimensional interval. We find a precise map between the geometry of dilaton and branes of type I' on the one hand and the geometry of real elliptic $K3$ on the other. We also argue more generally that strong coupling limits of string compactifications generically do not have a weakly coupled dual in terms of any known theory (as is exemplified by the strong coupling limit of heterotic strings in 9 dimensions for certain range of parameters).