Type I' and Real Algebraic Geometry

TL;DR

This paper explores the duality between type I' and heterotic strings in 9 dimensions, resolving perturbation theory puzzles and linking moduli space regions to real elliptic K3 surfaces, revealing limitations of weak coupling descriptions.

Contribution

It provides a detailed geometric analysis connecting type I' perturbation regions to real elliptic K3 surfaces and discusses the absence of weakly coupled duals at strong coupling limits.

Findings

Certain moduli regions are inaccessible via type I' perturbation theory.

All moduli regions correspond to real elliptic K3 surfaces in a specific limit.

Strong coupling limits often lack known weakly coupled dual descriptions.

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).