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

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,...

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Published in:arXiv.org 2023-01
Main Authors: Clingher, Adrian, Malmendier, Andreas
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Lattices
Parameterization
Strings
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description 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.
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subjects Lattices
Parameterization
Strings
title On the duality of F-theory and the CHL string in seven dimensions
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