An Instanton Toolbox for F-Theory Model Building
Joseph Marsano, Natalia Saulina, Sakura Schafer-Nameki
TL;DR
The paper addresses how to engineer key dimensionful scales in a local $SU(5)$ F-theory GUT by coupling singlet fields localized on D7-brane intersections to $D3$-instantons. The authors classify all supersymmetric $D3$-instantons that wrap the same $S_{GUT}$ as one of the D7-branes and intersect the GUT stack along a curve $Σ$ of genus $0$ or $1$, deriving topological conditions on $Σ$ governing which superpotential terms are generated. They show that such instantons can generate the SUSY-breaking scale and right-handed neutrino masses, while the μ-term is not produced directly, suggesting it should be tied to other scales. They also connect the linear superpotential construction to an O'Raifeartaigh-like model at the KK scale, whose 1-loop Coleman–Weinberg potential yields a metastable, long-lived SUSY-breaking vacuum. The paper provides explicit examples of linear, quadratic, and mixed instanton-induced couplings to realize these mechanisms within the two D7-brane on del Pezzo setup.
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 μterm 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 $Σ$ 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 Σfor 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.