= Stable zero-energy Polonyi vacuum
{title2=$\beta=2-\sqrt3,\quad\langle z\rangle=\sqrt3-1$}
For $m\ne0$ and positive $\beta$, the <Polonyi model> has a unique zero-energy <global minimum> at $\beta=2-\sqrt3$, $\langle z\rangle=\sqrt3-1$. Writing $u=\operatorname{Re}z-(\sqrt3-1)$ and $y=\operatorname{Im}z$, its potential bracket is $(u^2+y^2+\sqrt3u)^2+(2\sqrt3-3)u^2+(4-2\sqrt3)y^2$, a sum of nonnegative terms. The real and imaginary curvatures are $4\sqrt3$ and $8-4\sqrt3$. The other zero-energy <stationary point> with $\beta=2+\sqrt3$ and $z=-\sqrt3-1$ is a <saddle point>. The stable vacuum has nonzero <supergravity auxiliary field>, so it has <supersymmetry breaking> even with zero <cosmological constant>. The $m=0$ branch does not fix these values.
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