An Instanton Toolbox for F-Theory Model Building

TL;DR

This paper explores how D3-instantons in F-theory GUTs can generate key physical scales like supersymmetry breaking and neutrino masses, providing a systematic classification of instanton effects on intersecting D7-branes.

Contribution

It classifies instanton configurations on intersecting D7-branes in F-theory, linking topological conditions to model-building applications and analyzing their role in generating important physical scales.

Findings

D3-instantons can generate supersymmetry-breaking and neutrino mass scales.

Topological conditions on the intersection curve determine instanton contributions.

The construction relates to metastable SUSY-breaking vacua via O'Raifeartaigh models.

Abstract

Several dimensionful parameters needed for model building can be engineered in a certain class of SU(5) F-theory GUTs by adding extra singlet fields which are localized along pairwise intersections of D7-branes. The values of these parameters, however, depend on dynamics external to the GUT which causes the singlets to acquire suitable masses or expectation values. In this note, we demonstrate that D3-instantons which wrap the same 4-cycle as one of the intersecting D7's can provide precisely the needed dynamics to generate several important scales, including the supersymmetry-breaking scale and the right-handed neutrino mass. Furthermore, these instantons seem unable to directly generate the \mu term suggesting that, at least in this class of models, it should perhaps be tied to one of the other scales in the problem. More specifically, we study the simple system consisting of a pair of D7-branes wrapping del Pezzo surfaces which intersect along a curve $\Sigma$ of genus 0 or 1 and classify all instanton configurations which can potentially contribute to the superpotential. This allows one to formulate topological conditions which must be imposed on \Sigma for various model-building applications. Along the way, we also observe that the construction of arXiv:0808.1286 which engineers a linear superpotential in fact realizes an O'Raifeartaigh model at the KK scale whose 1-loop Coleman-Weinberg potential generically leads to a metastable, long-lived SUSY-breaking vacuum.