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In this note, we derive a Mellin space version of the Lorentzian inversionformula for CFTs by explicitly integrating over the cross-ratios in $d=2$ and$d=4$ spacetime dimensions. We use the simplicity of the Mellin representationof Witten diagrams and the double discontinuity to find the OPE coefficientsand anomalous dimensions of double-trace primaries in large $N$ CFTs to order$\frac{1}{N^4}$. We find that our results match analytically at order$\frac{1}{N^2}$, and numerically at order $\frac{1}{N^4}$ with existingliterature.

Lorentzian inversion and anomalous dimensions in Mellin space