Dynamically SUSY Breaking SQCD on F-Theory Seven-Branes

TL;DR

This work constructs a local F-theory model of ISS-style dynamical SUSY breaking using two intersecting seven-branes: one supports pure ${ m SU}(N_c)$ Yang-Mills, the other provides vector-bundle moduli whose dynamics control the masses of fundamental flavors living on the intersection curve. The key mechanism is that, by moving in the vector-bundle moduli space, a holomorphic determinant condition ${\det}f_{\cal C}=0$ is reached, yielding a tunable number of light flavors and hence SQCD in the free magnetic range with slightly massive quarks; the authors implement this explicitly on a rational elliptic surface ${dP}_9$ using the spectral-cover construction to encode the vector bundle data. They derive the associated quadratic superpotential $W=\lambda\,\phi\, {\rm Tr}(Q\tilde Q)$ that links bundle moduli to quark masses and provide concrete examples (e.g., ${N_c}=3$ with ${N_f}=4$, and ${N_c}=6$ with ${N_f}=8$) where massive SQCD in the free magnetic range emerges. The approach demonstrates a concrete string-theoretic embedding of ISS-like SUSY breaking and highlights the role of local geometry and moduli in controlling infrared dynamics, with potential extensions via brane instantons to generate small masses.

Abstract

We study how dynamically breaking SQCD can be obtained on two intersecting seven-branes in F-theory. In the mechanism which we present in this paper one of the seven-branes is responsible for producing the low-energy gauge group and the other one is for generating vector bundle moduli. The fundamental matter charged under the gauge group is localized on the intersection. The mass of the matter fields is controlled by the vector bundle moduli. The analysis of under what conditions a sufficient number of the fundamental flavors becomes light turns out to be equivalent to the analysis of non-perturbative superpotentials for vector bundle moduli in Heterotic M-theory. We give an example in which we present an explicit equation in the moduli space whose zero locus corresponds to the fundamental fields becoming light. This allows us to provide a local F-theory realization of massive ${\cal N}=1$, $SU(N_c)$ SQCD in the free magnetic range which dynamically breaks supersymmetry.