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On seven-brane dependent instanton prefactors in F-theory

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Abstract

We study the moduli-dependent prefactor of M5-instanton corrections to the superpotential in four-dimensional F-theory compactifications. In light of the M-theory and type IIb limits and also heterotic duality, we propose that the explicit moduli dependence of the prefactor can be computed by a study of zero modes localized at intersections between the instanton and seven-branes. We present an instanton prefactor in an E 6 F-theory GUT which does not admit a heterotic dual and show that it vanishes if and only if a point of E 8 enhancement is present in the instanton worldvolume. More generically, we discuss the relationship between points of E 8 and superpotential zeroes and give sufficient conditions for such a point to cause a zero, even for an SU(5) GUT. We scan a large class of compactifications for instanton physics and demonstrate that many instantons have the same prefactor structure. We discuss the associated implications and complications for moduli stabilization. We present an explicit resolution and construction of G-flux in a generic E 6 GUT and identify a global compactification of the local model spectral cover which happens to facilitate prefactor computations. Via a Leray spectral sequence, we demonstrate the relationship between right-movers of heterotic worldsheet instantons, 3-3 strings of euclidean D3 instantons, and the Fermi zero modes of M5-instantons.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Pennsylvania, 209 S. 33rd St, Philadelphia, PA, 19104, U.S.A.

    Mirjam Cvetič & James Halverson

  2. Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia

    Mirjam Cvetič

  3. Department of Mathematics, University of Pennsylvania, 209 S. 33rd St, Philadelphia, PA, 19104-6395, U.S.A.

    Ron Donagi

  4. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, U.S.A.

    James Halverson

  5. Enrico Fermi Institute, University of Chicago, 5640 S Ellis Ave, Chicago, IL, 60637, U.S.A.

    Joseph Marsano

  6. Sunrise Futures LLC, 30 S Wacker Suite 1706, Chicago, IL, 60606, U.S.A.

    Joseph Marsano

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  1. Mirjam Cvetič
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  2. Ron Donagi
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  4. Joseph Marsano
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Correspondence to James Halverson.

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Cvetič, M., Donagi, R., Halverson, J. et al. On seven-brane dependent instanton prefactors in F-theory. J. High Energ. Phys. 2012, 4 (2012). https://doi.org/10.1007/JHEP11(2012)004

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