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Mathematics Underlying the F-Theory/Heterotic String Duality in Eight Dimensions

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Abstract

We give an analytic description of the moduli space of classical vacua for F-theory compactified on elliptic K3 surfaces, on open tubular regions near the two Type II boundary divisors. The structure of these open sets is related to the total spaces of certain holomorphic theta fibrations over the corresponding boundary divisors. As the two Type II divisors can be naturally identified as moduli spaces of elliptic curves and flat G-bundles with G=(E8×E8)⋊ or Spin(32)/, one is led to an analytic isomorphism between these open domains and regions of the moduli spaces of heterotic string theory compactified on the two-torus corresponding to large volumes of the torus. This provides a proof for the classical version of F-theory/Heterotic String Duality in eight dimensions. A description of the Type II boundary points in terms of elliptic stable K3 surfaces is also given.

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Author notes

  1. John W. Morgan

    Present address: Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Adrian Clingher

  2. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    John W. Morgan

Authors
  1. Adrian Clingher
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  2. John W. Morgan
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Additional information

Communicated by M.R. Douglas

The first author was supported by NSF grants DMS-97-29992 and PHY-00-70928.

The second author was partially supported by NSF grant DMS-01-03877.

Acknowledgement The authors would like to thank Robert Friedman for many helpful conversations during the development of this work. The first author would also like to thank Charles Doran for many discussions regarding this work and the Institute for Advanced Study for its hospitality and financial support during the course of the academic year 2002–2003.

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Clingher, A., Morgan, J. Mathematics Underlying the F-Theory/Heterotic String Duality in Eight Dimensions. Commun. Math. Phys. 254, 513–563 (2005). https://doi.org/10.1007/s00220-004-1270-9

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