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.

arXiv comment40 pages

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Cited by in corpus (1)

• On two-elementary K3 surfaces with finite automorphism group