= Polonyi supersymmetry branches
{c}
{title2=$D_zW=m^2[1+\bar z(z+\beta)]$}
For the <Polonyi model> with canonical <Kähler potential> and $W=m^2(z+\beta)$, $\beta>0$, a constant <supersymmetric vacuum> with $m\ne0$ requires real $z=(-\beta\pm\sqrt{\beta^2-4})/2$ and exists exactly for $\beta\geq2$. Its <supergravity F-term potential> is negative because $W\ne0$. For $0<\beta<2$, the <supergravity auxiliary field> cannot vanish. If $m=0$, the model is flat with unbroken <supersymmetry>. This parameter-dependent statement is sharper than asserting that every linear <superpotential> breaks <supersymmetry> in <supergravity>.
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