= Nh^{N_f/N}\bigl(\Lambda_m^{-(N_f-3N)}\det(\Phi)\bigr)^{1/N}.\end{aligned}$$ Notice that the exponent of $\Lambda_m$, $-\left(N_f-3N\right)=-(3N_c-2N_f)$, is always negative in the free magnetic range. Hence the coefficient of the determinant grows as the cut-off shrinks.

Since the non-perturbative piece is R-symmetry violating a SUSY preserving minimum must exist [@Nelson:1993nf], created by the non-perturbative piece. In global SUSY [^2] this must be at a lower energy than the SUSY breaking minimum.

A note on dynamical scales
--------------------------

We now calculate the relationship between the dynamical scales, $\Lambda$ and $\Lambda_m$, of the electric and magnetic theories, respectively. We make use of the relevant part of the dictionary given in ISS’s paper and the duality relation, given by: $$\begin{aligned}
h= \frac{\sqrt{\alpha} \Lambda}{\widehat{\Lambda}}\end{aligned}$$ and $$\begin{aligned}
\Lambda^{3N_c-N_f}\Lambda_m^{2N_f-3N_c}=(-1)^{N_f-N_c}\widehat{\Lambda}^{N_f}.\end{aligned}$$ where $\hat{\Lambda}$ is a dimensional parameter in the magnetic theory, related to the electric quark mass, $m_0$, and the magnetic quark mass, $
\mu$ through the following relation: $\hat{\Lambda}=-\frac{\mu^2}{m_0}$

If we assume that the order one number, $\alpha$, appearing in the Kähler potential for the electric mesons [^3] is simply 1 and that $h=1$, then it follows that all three scales, $\Lambda$, $\Lambda_m$ and $\hat{\Lambda}$ are identified, up to flavour dependent phases. Above this scale the electric description is valid, while the magnetic description is 