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On the Duality of F-Theory and the CHL String in Seven Dimensions

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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.

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Notes

  1. The scenario has been recently claimed to be reconstructed in the Swampland Program in [4, 36], excluding the other disconnected components mentioned above.

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Acknowledgements

The authors would like to thank the referees for their insightful comments, in particular with regards to the correct physical interpretation of our results. A.C. acknowledges support from a UMSL Mid-Career Research Grant. A.M. acknowledges support from the Simons Foundation through grant no. 202367.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Missouri - St. Louis, St. Louis, MO, 63121, USA

    Adrian Clingher

  2. Department of Mathematics, University of Connecticut, Storrs, 06269, CT, USA

    Andreas Malmendier

  3. Department of Mathematics and Statistics, Utah State University, Logan, 84322, UT, USA

    Andreas Malmendier

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  1. Adrian Clingher
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Clingher, A., Malmendier, A. On the Duality of F-Theory and the CHL String in Seven Dimensions. Commun. Math. Phys. 393, 631–667 (2022). https://doi.org/10.1007/s00220-022-04374-1

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