Vacuum structure of spontaneously broken N=2 supersymmetric gauge theory

TL;DR

This paper investigates the vacuum structure of N=2 supersymmetric gauge theories with Fayet-Iliopoulos terms, revealing how quantum effects lift classical degeneracies and can lead to metastable vacua with broken supersymmetry.

Contribution

It provides a detailed analysis of quantum corrections in SU(2)×U(1) gauge theories with massless hypermultiplets, showing the emergence of local minima with broken supersymmetry.

Findings

Classical vacuum degeneracy is lifted by quantum effects.

In N_f=1 case, the effective potential exhibits runaway behavior.

In N_f=2 case, a local minimum with broken supersymmetry can appear.

Abstract

We analyze the vacuum structure of spontaneously broken N=2 supersymmetric gauge theory with the Fayet-Iliopoulos term. Our theory is based on the gauge group SU(2) \times U(1) with N_f=1,2 massless quark hypermultiplets having the same U(1) charges. In the classical potential, there are degenerate vacua even in the absence of supersymmetry. It is shown that this vacuum degeneracy is smoothed out, once quantum corrections are taken into account. In N_f=1 case, the effective potential is found to be so-called runaway type, and there is neither well-defined vacuum nor local minimum. On the other hand, in N_f=2 case, while there is also the runaway direction in the effective potential, we find the possibility that there appears the local minimum with broken supersymmetry at the degenerate dyon point.