Metastable vacua in perturbed Seiberg–Witten theories. Part 2: Fayet–Iliopoulos terms and Kähler normal coordinates Original Research Article

We show that the perturbation of an image supersymmetric gauge theory by a superpotential linear in the Kähler normal coordinates of the Coulomb branch, discussed in [H. Ooguri, Y. Ookouchi, C.S. Park, Metastable vacua in perturbed Seiberg–Witten theories, arXiv: 0704.3613 [hep-th]], 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 image 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. Relations of these constructions to flux compactifications and geometric meta-stability are also discussed.