Lorentzian inversion and anomalous dimensions in Mellin space

In this note, we derive a Mellin space version of the Lorentzian inversion formula for CFTs by explicitly integrating over the cross-ratios in d = 2 and d = 4 spacetime dimensions. We use the simplicity of the Mellin representation of Witten diagrams and the double discontinuity to find the OPE coefficients and anomalous dimensions of double- trace primaries in large N CFTs to order 1N4. We find that our results match analytically at order 1N2, and numerically at order 1N4 with existing literature.