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).

71 pages and 16 figures

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Cited by in corpus (14)

• Supergravity duals of gauge theories from F(4) gauged supergravity in six dimensions
• Heterotic/Type II Triality and Instantons on $K_3$
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• The Moduli Space and M(atrix) Theory of 9d N=1 Backgrounds of M/String Theory
• A new twist on heterotic string compactifications
• On Heterotic Orbifolds, M Theory and Type I' Brane Engineering
• On the Strong Coupling Dynamics of heterotic string theory on C^3/Z_3
• F-theory Duals of M-theory on G2 Manifolds from Mirror Symmetry
• Gauged Supergravities from Spherical Reductions
• TASI Lectures on Compatification and Duality
• Determining the dual
• A comment on 4d and 5d BPS states
• Shift orbifolds, decompactification limits, and lattices