Potential analysis of N=2 SUSY gauge theory with the Fayet-Iliopoulos term

TL;DR

This paper investigates the vacuum structure of an N=2 supersymmetric SU(2) x U(1) gauge theory with Fayet-Iliopoulos term, revealing quantum effects that lift classical degeneracy and suggest a local minimum with broken supersymmetry.

Contribution

It provides a quantum analysis of vacuum degeneracy and potential supersymmetry breaking in a specific N=2 gauge theory with Fayet-Iliopoulos term.

Findings

Quantum corrections lift classical vacuum degeneracy.

Existence of a local minimum with broken supersymmetry.

Runaway directions in the effective potential.

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=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. While there is the runaway direction in the effective potential, we found the promising possibility that there appears the local minimum with broken supersymmetry at the degenerate dyon point.