Meta-stable Vacuum in Spontaneously Broken N=2 Supersymmetric Gauge Theory

TL;DR

This paper studies a meta-stable vacuum in an N=2 supersymmetric gauge theory with spontaneous supersymmetry breaking, quantum corrections, and potential implications for gauge mediation in particle physics.

Contribution

It demonstrates the existence of a long-lived, meta-stable vacuum in an N=2 gauge theory with FI term, with potential applications to phenomenology.

Findings

Quantum corrections remove classical vacuum degeneracy.

A local minimum at the dyon point breaks supersymmetry and U(1)_R symmetry.

The meta-stable vacuum is parametrically long-lived.

Abstract

We consider an N=2 supersymmetric SU(2) \times 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 pseudo-flat direction in the classical potential. This vacuum degeneracy is removed once quantum corrections are taken into account. Due to 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 meta-stable 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.