Metastable Vacua in Perturbed Seiberg-Witten Theories, Part 2: Fayet-Iliopoulos Terms and K\"ahler Normal Coordinates

Understand

We show that the perturbation of an N=2 supersymmetric gauge theory by a superpotential linear in the Kahler normal coordinates of the Coulomb branch, discussed in arXiv:0704.3613, is equivalent to the perturbation by Fayet-Iliopoulos terms.

• It follows that the would-be meta-stable vacuum at the origin of the normal coordinates in fact preserves N=1 supersymmetry unless the superpotential is truncated to a finite-degree polynomial of the adjoint scalar fields.
• We examine the criteria for supersymmetry breaking under a perturbation by Fayet-Iliopoulos terms and present a general classification of non-supersymmetric critical points.
• In some explicit examples, we are also able to study local stability of these points and demonstrate that, if the perturbation is chosen appropriately, they indeed correspond to supersymmetry-breaking vacua.