in the SM. On the other hand for $m^2>0$ the constraint is only obeyed for $\phi^2>(2/3)m^2$.

A simple class of SUSY superpotentials is the exponential one, $W=e^{-\alpha M}$, with $M$ a canonically normalized complex scalar. The condition may be written as 2(V\_[MM\^\*M\^\*]{})(V\_[M\^\*MM]{}) - (V\_[MM\^\*]{})(V\_[MMM\^\*M\^\*]{})    . It is easy to check that this exponential superpotential leads to a potential passing the SSWGC constraint as long as $|\alpha |\geq 1/M_{\text{p}}^2$, for any value of $M$. One can also test a cubic superpotential which may appear in e.g. in string flux compactifications, i.e. W(T) = T\^2 + T\^3  . The differential inequation yields \^2     . One sees that trans-Planckian trips of $T$ would in this case violate the bound. And also the scalar interaction coupling is bounded below by $\lambda^2 \geq \frac {m^2}{M_{\text{p}}^2}$. This is consistent with the idea that gravity must be the weakest force. Let us comment that in fact instead of the global SUSY potential one should have used the $N=1$ supergravity potential. However this does not modify the result because the additional terms in the potential have an extra Planck mass supression.

 Applications
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The above introduced Strong SWGC may have an important impact whenever there is some Planck 