Duality in the Presence of Supersymmetry Breaking

TL;DR

The paper investigates Seiberg duality in ${\cal N}=1$ SQCD when soft SUSY breaking is introduced via a shared dynamical SUSY-breaking sector, using gauge mediation and a canonical Kähler potential. The authors compute the induced soft masses in both electric and magnetic theories, finding that many scalar masses in the magnetic theory are tachyonic and drive distinct symmetry-breaking patterns; a notable IR sum rule ${X=\tilde m_q^2+\tilde m_{ar q}^2+\tilde m_M^2\to 0}$ emerges for small breaking. Depending on the regime (magnetic free, Banks–Zaks fixed point, or completely higgsed dual), the signs of soft masses and the resulting vacua differ, with some cases suggesting breakdowns of the duality when mapped to non-supersymmetric QCD. The results depend on messenger content and the canonical-Kähler assumption, and the study highlights potential phase transitions or limits where dual descriptions cease to describe the same IR physics under substantial SUSY breaking.

Abstract

We study Seiberg duality for N=1 supersymmetric QCD with soft supersymmetry-breaking terms. We generate the soft terms through gauge mediation by coupling two theories related by Seiberg duality to the same supersymmetry-breaking sector. In this way, we know what a supersymmetry-breaking perturbation in one theory maps into in its ``dual''. Assuming a canonical Kahler potential we calculate the soft terms induced in the magnetic theory and find that some of the scalars acquire negative masses squared. If duality is still good for small supersymmetry breaking, this may imply some specific symmetry breaking patterns for supersymmetric QCD with small soft supersymmetry-breaking masses, in the case that its dual theory is weakly coupled in the infrared. In the limit of large supersymmetry breaking, the electric theory becomes ordinary QCD. However, the resulting symmetry breaking in the magnetic theory is incompatible with that expected for QCD.