= Three-point worldsheet ghost correlator
{title2=$\langle c(z_1)c(z_2)c(z_3)\rangle=z_{12}z_{13}z_{23}$}
On the <Riemann sphere>, three holomorphic reparameterization ghost zero modes correspond to the three infinitesimal <Möbius transformations>. Three $c$ insertions saturate their <Grassmann integral>. In a basis $1,z,z^2$, their integral is the Vandermonde determinant, giving $z_{12}z_{13}z_{23}$ up to an ordering-dependent sign. Including the antiholomorphic factor gives $|z_{12}z_{13}z_{23}|^2$, the Jacobian in <sphere gauge fixing for four string vertices>.
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