= Global conformal Ward identities for chiral correlators
For <primary operators> of holomorphic weights $h_i$ and a <Möbius transformation> invariant vacuum, infinitesimal translations, dilations and special conformal transformations give $\sum_i\partial_iG=0$, $\sum_i(z_i\partial_i+h_i)G=0$, and $\sum_i(z_i^2\partial_i+2h_i z_i)G=0$. Solving gives a constant one-point function only at $h=0$, a two-point function $Cz_{12}^{-2h}$ only for equal weights, and a three-point function $Cz_{12}^{h_3-h_1-h_2}z_{13}^{h_2-h_1-h_3}z_{23}^{h_1-h_2-h_3}$. Three-point covariance imposes no further equality of weights; dynamical selection rules may still force $C=0$. For more points, arbitrary functions of <conformal cross-ratios> remain.
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