= Matter-logarithm no-scale potential
{title2=$V=e^K\left(s^2|D_SW|^2+\frac t3|W_C|^2\right)$}
For $s=S+\bar S>0$, $t=T+\bar T-|C|^2>0$, $K=-\log s-3\log t$ and a holomorphic <superpotential> independent of $T$, the exact <F-term> potential is $V=e^K[s^2|D_SW|^2+(t/3)|W_C|^2]$. Inverting the mixed $T,C$ metric gives $K^{T\bar T}=t(t+|C|^2)/3$, $K^{T\bar C}=t\bar C/3$, $K^{C\bar T}=tC/3$, and $K^{C\bar C}=t/3$. Substitution of $D_TW=-3W/t$ and $D_CW=W_C+3\bar CW/t$ cancels all mixed terms, leaving $3|W|^2+(t/3)|W_C|^2$; the first term cancels the <supergravity> negative term.
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