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

TL;DR

This paper explores how perturbations by Fayet-Iliopoulos terms affect supersymmetry in perturbed Seiberg-Witten theories, showing conditions for supersymmetry preservation or breaking and analyzing stability of vacua.

Contribution

It establishes the equivalence between superpotential perturbations in Kahler normal coordinates and Fayet-Iliopoulos terms, providing a classification of supersymmetry-breaking critical points.

Findings

Superpotential perturbations are equivalent to Fayet-Iliopoulos terms.

Certain perturbations preserve N=1 supersymmetry, others break it.

Explicit examples demonstrate conditions for stable supersymmetry-breaking vacua.

Abstract

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. Relations of these constructions to flux compactifications and geometric meta-stability are also discussed.