Instantons and SUSY breaking in F-theory
Jonathan J. Heckman, Joseph Marsano, Natalia Saulina, Sakura Schafer-Nameki, Cumrun Vafa
TL;DR
The paper investigates non-perturbative instanton effects in local F-theory compactifications as a mechanism for dynamical SUSY breaking. It analyzes Euclidean D3-instantons bound to 7-branes, counting zero modes and using both perturbative string theory and a topologically twisted worldvolume description, with exact matches between approaches. It establishes a Polonyi-like model generated by a D3-instanton and shows subleading multi-instanton corrections, including a novel one-instanton contribution to the glueball superpotential in 4d $SU(N)$ gauge theory, offering routes to moduli stabilization and SUSY breaking. The work connects arithmetic genus constraints, flux trivializability, and higher-dimensional instanton interpretations to provide a framework for generating hierarchically small SUSY-breaking effects in F-theory GUT contexts, potentially enabling explicit, stringy SUSY-breaking sectors that couple to the visible sector.
Abstract
We study instanton contributions to the superpotential of local F-theory compactifications which could potentially be used to engineer models of dynamical supersymmetry breaking. These instantons correspond to Euclidean 3-branes which form a threshold bound state with spacetime filling 7-branes. In certain cases, their contributions to the effective 4d superpotential can be determined in both perturbative string theory as well as directly via the topologically twisted theory on the 3-brane worldvolume, and in all cases we observe an exact match between these results. We further present an instanton generated Polonyi-like model, and characterize subleading corrections to the superpotential which arise from multi-instantons. We also study instanton contributions to 4d pure N=1 SU(N) gauge theory realized by a stack of 7-branes wrapping a rigid 4-cycle and find that there is a non-trivial contribution to the glueball superpotential from the single instanton sector. This correction is absent in the purely 4d theory and could conceivably be used either to stabilize moduli or to break supersymmetry.