Metastable vacuum in spontaneously brokenN=2supersymmetric gauge theory

Abstract

We consider an $\mathcal{N}=2$ supersymmetric $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ gauge theory with ${N}_{f}=2$ massless flavors and a Fayet-Iliopoulos (FI) term. In the presence of the FI term, supersymmetry is spontaneously broken at tree level (on the Coulomb branch), leaving a pseudoflat direction in the classical potential. This vacuum degeneracy is removed once quantum corrections are taken into account. Because of the $SU(2)$ gauge dynamics, the effective potential exhibits a local minimum at the dyon point, where not only supersymmetry but also $U(1{)}_{R}$ symmetry is broken, while a supersymmetric vacuum would be realized toward infinity with the runaway behavior of the potential. This local minimum is found to be parametrically long-lived. Interestingly, from a phenomenological point of view, in this metastable vacuum the massive hypermultiplets inherent in the theory play the role of the messenger fields in the gauge mediation scenario, when the standard model gauge group is embedded into their flavor symmetry.