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On Instanton Effects in F-theory

Ralph Blumenhagen, Andres Collinucci, Benjamin Jurke

Abstract

We revisit the issue of M5-brane instanton corrections to the superpotential in F-theory compactifications on elliptically fibered Calabi-Yau fourfolds. Elaborating on concrete geometries, we compare the instanton zero modes for non-perturbative F-theory models with the zero modes in their perturbative Sen limit. The fermionic matter zero modes localized on the intersection of the instanton with the space-time filling D7-branes show up in a geometric way in F-theory. Methods for their computation are developed and, not surprisingly, exceptional gauge group structures do appear. Finally, quite intriguing geometrical aspects of the one-loop determinant are discussed.

On Instanton Effects in F-theory

Abstract

We revisit the issue of M5-brane instanton corrections to the superpotential in F-theory compactifications on elliptically fibered Calabi-Yau fourfolds. Elaborating on concrete geometries, we compare the instanton zero modes for non-perturbative F-theory models with the zero modes in their perturbative Sen limit. The fermionic matter zero modes localized on the intersection of the instanton with the space-time filling D7-branes show up in a geometric way in F-theory. Methods for their computation are developed and, not surprisingly, exceptional gauge group structures do appear. Finally, quite intriguing geometrical aspects of the one-loop determinant are discussed.

Paper Structure

This paper contains 18 sections, 142 equations, 7 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Instantons in Type IIB and F-theory
  3. Uncharged zero modes
  4. The orientifold geometry
  5. $O(1)$ E3-brane instantons
  6. $U(1)$ E3-brane instantons
  7. F-theory uplift
  8. Non-recombining $U(1)$ instantons in F-theory
  9. Charged zero modes
  10. Matter zero modes from smooth $\Delta_a$
  11. Matter zero modes from $\Delta_R$
  12. Phenomenological consequences
  13. Counting three-cycles on the M5-brane
  14. Three-cycles and the M5 partition function
  15. Conclusion
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Geometric setting
  • Figure 2: single $O(1)$ D7-brane - $U(1)$ brane/image-brane pair
  • Figure 3: single $O(1)$ E3-brane - $U(1)$ brane/image-brane pair
  • Figure 4: The even cohomologies of the E3 travel horizontally, whereas the odd ones are raised to forms of the M5 of one degree higher .
  • Figure 5: $SU(n)$ matter zero mode curves and Yukawa-type interactions in surface $\mathcal{E}\subset \mathcal{M}$
  • ...and 2 more figures