On the duality of F-theory and the CHL string in seven dimensions

Abstract

We show that the duality between F-theory and the CHL string in seven dimensions defines algebraic correspondences between K3 surfaces polarized by the rank-ten lattices $H\oplus N$ and $H\oplus E_8(-2)$. In the special case when the F-theory admits an additional anti-symplectic involution or, equivalently, the CHL string admits a symplectic one, both moduli spaces coincide. In this case, we derive an explicit parametrization for the F-theory compactifications dual to the CHL string, using an auxiliary genus-one curve, based on a construction given by André Weil.

40 pages

References in corpus (5)

• 8d Supergravity, Reconstruction of Internal Geometry and the Swampland
• K3 surfaces, modular forms, and non-geometric heterotic compactifications
• Discrete gauge groups in certain F-theory models in six dimensions
• Non-Geometric F-Theory-Heterotic Duality
• The duality between F-theory and the Heterotic String in $D=8$ with two Wilson lines

Cited by in corpus (1)

• On two-elementary K3 surfaces with finite automorphism group